geothms0201

3 Undefined variable. (Line: 7, position: 11)

25 Undefined variable. (Line: 6, position: 11)

44 Undefined variable. (Line: 9, position: 12)

50 Wrong variable type. (Line: 6, position: 13)

77 Warning: fread() 

86 Warning: fread()


geothms0301 - gclc 7.1



Elementos

INSERT INTO theorems (teoId,userId,category,description,shortDescription,teoName,dateSubmission) VALUES ('GEO0001','gpreda1 ','Geometry','\\begin{geothm} Given four points $A$, $B$, $C$ and $D$, points of intersections are formed: $L = AB \\cap CD$, $K = AC \\cap BC$, $F = KL \\cap BD$ and $G = KL \\cap AC$. Show that segment $KL$ is harmonically divided by the points $F$ and $G$, ie: $\\frac{\\overline{LK}}{\\overline{KF}} = \\frac{\\overline{GL}}{\\overline{GF}}$. \\end{geothm}',' ', ' Harmonic Points ','2008/01/09')

INSERT INTO figures (teoId,drawerId,code,dateSubmission,bibref,userId) VALUES ('GEO0001','3',' dim 130 100 point A 52 20 point B 72 20 point C 66 40 point D 56 36 cmark_b A cmark_b B cmark_r C cmark_lt D line AB A B line CD C D intersec L AB CD cmark_b L line AD A D line BC B C intersec K AD BC cmark_lt K line BD B D line KL K L intersec F BD KL cmark_lt F line AC A C intersec G AC KL cmark_lt G drawsegment B L drawsegment C L drawsegment A K drawsegment B K drawsegment B F drawsegment A G line lkfg L K drawdashline lkfg ','2008/01/09','', 'gpreda1 ')
gclc figure0001.code figure0001.pic > figure0001.errors
Warning: fread() [function.fread]: Length parameter must be greater than 0 in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 328
Figura 0

    * Figure
    * figure0001.jpg
    * Description of the construction in natural language
    * figure0001.xml
    * Figure in SVG format
    * figure0001.svg

INSERT INTO demonstrations (teoId,proverId,code,dateSubmission,bibref,userId) VALUES ('GEO0001','2',' point A 52 20 point B 72 20 point C 66 40 point D 56 36 line AB A B line CD C D intersec L AB CD line AD A D line BC B C intersec K AD BC line BD B D line KL K L intersec F BD KL line AC A C intersec G AC KL prove { harmonic L K F G } ','2008/01/09', '','gpreda1 ')
The Proof's code 0001 is correct.

Processing the XML file, please wait
/usr/local/bin/gclc proof0001.code proofCode0001.xml -xml > proof0001.errors
Warning: fread() [function.fread]: Length parameter must be greater than 0 in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 497

INSERT INTO theorems (teoId,userId,category,description,shortDescription,teoName,dateSubmission) VALUES ('GEO0002','gpreda1 ','Geometry','\\begin{geothm} Two lines, $AB$ and $CD$ intersect at a point $O$. If $AC \\parallel DB$, show that: $\\frac{\\overline{OA}}{\\overline{OB}} = \\frac{\\overline{OC}}{\\overline{OD}}$ \\end{geothm}',' ', ' Thales Theorem ','2008/01/09')

INSERT INTO figures (teoId,drawerId,code,dateSubmission,bibref,userId) VALUES ('GEO0002','3',' dim 80 80 point O 20 30 point A 60 30 point C 40 50 point B 35 30 line a A C line c O C parallel b B a intersec D c b drawline O A drawline O C drawline A C drawline B D cmark_t O cmark_t A cmark_t B cmark_t C cmark_t D ','2008/01/09','', 'gpreda1 ')
gclc figure0002.code figure0002.pic > figure0002.errors
Warning: fread() [function.fread]: Length parameter must be greater than 0 in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 328
Figura 8

    * Figure
    * figure0002.jpg
    * Description of the construction in natural language
    * figure0002.xml
    * Figure in SVG format
    * figure0002.svg

INSERT INTO demonstrations (teoId,proverId,code,dateSubmission,bibref,userId) VALUES ('GEO0002','2',' point O 20 30 point A 60 30 point C 40 50 online B O A line a A C line c O C parallel b B a intersec D c b prove { equal { sratio O A O B } { sratio O C O D } } ','2008/01/09', '','gpreda1 ')
The Proof's code 0002 is correct.

Processing the XML file, please wait
/usr/local/bin/gclc proof0002.code proofCode0002.xml -xml > proof0002.errors
Warning: fread() [function.fread]: Length parameter must be greater than 0 in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 497

INSERT INTO theorems (teoId,userId,category,description,shortDescription,teoName,dateSubmission) VALUES ('GEO0003','gpreda1 ','Geometry','\\begin{geothm} Given triangle $ABC$, let $p$ be line through $A$ parallel with $BC$, and let $q$ be line through $C$ parallel with $AB$. Let $p$ and $q$ intersects at $D$. Show that $\\overline{AB} = \\overline{DC}$. \\end{geothm}',' ', ' Parallelogram Theorem ','2008/01/09')

INSERT INTO figures (teoId,drawerId,code,dateSubmission,bibref,userId) VALUES ('GEO0003','3',' dim 130 70 point A 20 20 point B 80 20 point C 103.40 55.10 line ab A B line bc B C parallel p A bc parallel q C ab intersec D p q cmark_b A cmark_b B cmark_t C cmark_t D drawsegment A B drawsegment C B drawsegment A D drawsegment C D ','2008/01/09','', 'gpreda1 ')
gclc figure0003.code figure0003.pic > figure0003.errors
Warning: fread() [function.fread]: Length parameter must be greater than 0 in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 328
Figura 16

    * Figure
    * figure0003.jpg
    * Description of the construction in natural language
    * figure0003.xml
    * Figure in SVG format
    * figure0003.svg

INSERT INTO demonstrations (teoId,proverId,code,dateSubmission,bibref,userId) VALUES ('GEO0003','2',' point A 20 20 point B 80 20 point C 103.40 55.10 line ab A B line bc B C parallel p A bc parallel q C ab intersec D p q prove { equal { sratio A B D C } { 1 } } ','2008/01/09', '','gpreda1 ')
The Proof's code 0003 is correct.

Processing the XML file, please wait
/usr/local/bin/gclc proof0003.code proofCode0003.xml -xml > proof0003.errors
Warning: fread() [function.fread]: Length parameter must be greater than 0 in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 497

INSERT INTO theorems (teoId,userId,category,description,shortDescription,teoName,dateSubmission) VALUES ('GEO0004','gpreda1 ','Geometry','\\begin{geothm} Let $ABC$ be an equilateral triangle inscribed in a circle with center $O$, and let $P$ be any point on the circle. Then the Simson line of $P$ bisects the radius $OP$. \\end{geothm}',' ', ' Example 35 ','2008/01/09')

INSERT INTO bibtheorem (teoId,bibrefId) VALUES ('GEO0004','chou88')

INSERT INTO figures (teoId,drawerId,code,dateSubmission,bibref,userId) VALUES ('GEO0004','3',' dim 130 110 point A 30 30 point B 100 30 circle k1 A B med mc A B intersec2 C C1 k1 mc med mb A C intersec O mc mb circle k O A point P 105.25 53.81 line cb C B line ac A C foot D P cb foot E P ac line de D E line po P O intersec I po de cmark_b I drawline de cmark_b A cmark_b B cmark_t C cmark_t O cmark_r P cmark_rt D cmark_l E drawdashsegment P O drawcircle k drawsegment A B drawsegment A C drawsegment C B ','2008/01/09','chou88', 'gpreda1 ')
gclc figure0004.code figure0004.pic > figure0004.errors
Warning: fread() [function.fread]: Length parameter must be greater than 0 in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 328
Figura 24

    * Figure
    * figure0004.jpg
    * Description of the construction in natural language
    * figure0004.xml
    * Figure in SVG format
    * figure0004.svg

INSERT INTO demonstrations (teoId,proverId,code,dateSubmission,bibref,userId) VALUES ('GEO0004','2',' point A 30 30 point B 100 30 circle k1 A B med mc A B intersec2 C C1 k1 mc med mb A C intersec O mc mb circle k O A oncircle P O A line cb C B line ac A C foot D P cb foot E P ac line de D E line po P O intersec I po de prove { equal { sratio O I I P } { 1 } } ','2008/01/09', '','gpreda1 ')
The Proof's code 0004 is correct.

Processing the XML file, please wait
/usr/local/bin/gclc proof0004.code proofCode0004.xml -xml > proof0004.errors
Warning: fread() [function.fread]: Length parameter must be greater than 0 in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 497

INSERT INTO theorems (teoId,userId,category,description,shortDescription,teoName,dateSubmission) VALUES ('GEO0005','gpreda1 ','Geometry','\\begin{geothm} Starting from five points $A$, $B$, $C$, $D$ and $E$ with $A$, $B$, $C$ collinear, new lines and points of intersection are formed. $ED$, $IG$, $LK$ and $JH$ are collinear. \\end{geothm}',' ', ' Example 3 ','2008/01/09')

INSERT INTO bibtheorem (teoId,bibrefId) VALUES ('GEO0005','chou88')

INSERT INTO figures (teoId,drawerId,code,dateSubmission,bibref,userId) VALUES ('GEO0005','3',' dim 100 100 point A 20 20 point B 55 20 line ab A B point C 50 20 point D 40.20 47.20 point E 53.30 37.50 line ae A E line cd C D line ad A D line be B E line bd B D line ec E C line de D E intersec J ae cd intersec G ad be intersec K bd ec intersec I ae bd intersec L cd be intersec H ec ad intersec F de ab line jh J H line ig I G intersec O jh ig cmark_rb A cmark_b B cmark_lb C cmark_t D cmark_rb E cmark_lb J cmark_lt G cmark_r K cmark_b I cmark_r L cmark_rb H cmark_b F cmark_r O line oed O E line olk O L drawline oed drawline olk drawdashline ab drawdashline ae drawdashline cd drawdashline ad drawdashline ec drawdashsegment I G drawdashsegment J H ','2008/01/09','chou88', 'gpreda1 ')
gclc figure0005.code figure0005.pic > figure0005.errors
Warning: fread() [function.fread]: Length parameter must be greater than 0 in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 328
Figura 32

    * Figure
    * figure0005.jpg
    * Description of the construction in natural language
    * figure0005.xml
    * Figure in SVG format
    * figure0005.svg

INSERT INTO demonstrations (teoId,proverId,code,dateSubmission,bibref,userId) VALUES ('GEO0005','2',' point A 20 20 point B 55 20 line ab A B online C A B point D 40.20 47.20 point E 53.30 37.50 line ae A E line cd C D line ad A D line be B E line bd B D line ec E C line de D E intersec J ae cd intersec G ad be intersec K bd ec intersec I ae bd intersec L cd be intersec H ec ad intersec F de ab line jh J H line ig I G intersec O jh ig prove { collinear O E D } prove { collinear O L K } ','2008/01/09', '','gpreda1 ')
The Proof's code 0005 is correct.

Processing the XML file, please wait
/usr/local/bin/gclc proof0005.code proofCode0005.xml -xml > proof0005.errors
Warning: fread() [function.fread]: Length parameter must be greater than 0 in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 497

INSERT INTO theorems (teoId,userId,category,description,shortDescription,teoName,dateSubmission) VALUES ('GEO0006','gpreda1 ','Geometry','\\begin{geothm} In a cyclic quadrilateral having perpendicular diagonals, the perpendicular to a side from the point of intersection of the diagonals always bisects the opposite side. \\end{geothm}',' ', ' Brahmagupta s Theorem ','2008/01/09')

INSERT INTO bibtheorem (teoId,bibrefId) VALUES ('GEO0005','chou88')

INSERT INTO figures (teoId,drawerId,code,dateSubmission,bibref,userId) VALUES ('GEO0006','3',' dim 110 110 point B 20 40 point T 43 40 point O 55 60 circle k O B line bd B T perp ac T bd perp ob O bd intersec X ob bd towards D B X 2 intersec2 A C1 k ac perp oa O ac intersec Y oa ac towards C A Y 2 line ad A D line bc B C perp tp T bc intersec P tp ad intersec Q tp bc cmark_rt P cmark_t Q cmark_l B cmark_r D cmark_t A cmark_b C cmark_b O cmark_rb T cmark_b X cmark_l Y drawdashsegment P Q drawsegment A B drawsegment C B drawsegment C D drawsegment A D drawsegment A C drawsegment D B drawcircle k ','2008/01/09','', 'gpreda1 ')
gclc figure0006.code figure0006.pic > figure0006.errors
Warning: fread() [function.fread]: Length parameter must be greater than 0 in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 328
Figura 40

    * Figure
    * figure0006.jpg
    * Description of the construction in natural language
    * figure0006.xml
    * Figure in SVG format
    * figure0006.svg

INSERT INTO demonstrations (teoId,proverId,code,dateSubmission,bibref,userId) VALUES ('GEO0006','2',' point B 20 40 point T 43 40 point O 55 60 circle k O B line bd B T perp ac T bd perp ob O bd intersec X ob bd towards D B X 2 intersec2 A C1 k ac perp oa O ac intersec Y oa ac towards C A Y 2 line ad A D line bc B C perp tp T bc intersec P tp ad intersec Q tp bc prove { equal { sratio A P P D } { 1 } } ','2008/01/09', '','gpreda1 ')
The Proof's code 0006 is correct.

Processing the XML file, please wait
/usr/local/bin/gclc proof0006.code proofCode0006.xml -xml > proof0006.errors
Warning: fread() [function.fread]: Length parameter must be greater than 0 in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 497

INSERT INTO theorems (teoId,userId,category,description,shortDescription,teoName,dateSubmission) VALUES ('GEO0007','gpreda1 ','Geometry','\\begin{geothm} Triangle $ABC$ and point $O$ are given. Let $p$, $q$ and $r$ be lines through the point $O$ which are perpendicular with lines $OA$, $OB$ and $OC$ respectively. Let $D$, $E$, and $F$ be intersections of lines $p$, $q$ and $r$ with lines $BC$, $AC$ and $BC$ respectively. Show that $D$, $E$ and $F$ are collinear. \\end{geothm}',' ', ' Dual Altitude Theorem ','2008/01/09')

INSERT INTO bibtheorem (teoId,bibrefId) VALUES ('GEO0005','chou88')

INSERT INTO figures (teoId,drawerId,code,dateSubmission,bibref,userId) VALUES ('GEO0007','3',' dim 100 80 point A 20 20 point B 80 20 point C 40 60 point O 75 45 line bc B C line ca C A line ab A B line oa O A perp od O oa intersec D od bc line ob O B perp oe O ob intersec E oe ca line oc O C perp of O oc intersec F of ab cmark_b A cmark_b B cmark_t C cmark_r O cmark_b D cmark_t E cmark_b F drawsegment A B drawsegment D C drawsegment C A drawsegment O A drawsegment O B drawsegment O C drawdashsegment O E drawdashsegment O F drawdashsegment O D line def D E drawdashline def ','2008/01/09','', 'gpreda1 ')
gclc figure0007.code figure0007.pic > figure0007.errors
Warning: fread() [function.fread]: Length parameter must be greater than 0 in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 328
Figura 48

    * Figure
    * figure0007.jpg
    * Description of the construction in natural language
    * figure0007.xml
    * Figure in SVG format
    * figure0007.svg

INSERT INTO demonstrations (teoId,proverId,code,dateSubmission,bibref,userId) VALUES ('GEO0007','2',' point A 20 20 point B 80 20 point C 40 60 point O 75 45 line bc B C line ca C A line ab A B line oa O A perp od O oa intersec D od bc line ob O B perp oe O ob intersec E oe ca line oc O C perp of O oc intersec F of ab line def D E prove { collinear D E F } ','2008/01/09', '','gpreda1 ')
The Proof's code 0007 is correct.

Processing the XML file, please wait
/usr/local/bin/gclc proof0007.code proofCode0007.xml -xml > proof0007.errors
Warning: fread() [function.fread]: Length parameter must be greater than 0 in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 497

INSERT INTO theorems (teoId,userId,category,description,shortDescription,teoName,dateSubmission) VALUES ('GEO0008','gpreda1 ','Geometry','\\begin{geothm} Given points $O$, $A$, $B$, $C$ and $O_1$ new points are constructed as: $A_1 = O_1B \\cap OC$, $B_1 = OA \\cap O_1C$, $C_1 = OB \\cap O_1A$, $I = BB_1 \\cap AA_1$. Show that points $C$, $C_1$ and $I$ are collinear. \\end{geothm}',' ', ' Pappus Dual Theorem ','2008/01/09')

INSERT INTO bibtheorem (teoId,bibrefId) VALUES ('GEO0005','chou88')

INSERT INTO figures (teoId,drawerId,code,dateSubmission,bibref,userId) VALUES ('GEO0008','3',' dim 130 130 point O 25.80 48.30 point A 95.20 55.00 point B 120.10 91.60 point C 44.50 112.70 point O_1 62.40 56.80 line o1b O_1 B line oc O C line oa O A line o1c O_1 C line ob O B line o1a O_1 A intersec A_1 o1b oc intersec B_1 oa o1c line bb1 B B_1 line aa1 A A_1 intersec C_1 ob o1a intersec I bb1 aa1 line cc1i C I drawdashline cc1i cmark_b A_1 cmark_rb B_1 cmark_lt C_1 cmark_rb I cmark_l O cmark_b A cmark_b B cmark_l C cmark_lt O_1 drawsegment A_1 C drawsegment O B drawsegment O A drawsegment A C_1 drawsegment A_1 B drawsegment C B_1 drawdashsegment A_1 A drawdashsegment I B ','2008/01/09','', 'gpreda1 ')
gclc figure0008.code figure0008.pic > figure0008.errors
Warning: fread() [function.fread]: Length parameter must be greater than 0 in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 328
Figura 56

    * Figure
    * figure0008.jpg
    * Description of the construction in natural language
    * figure0008.xml
    * Figure in SVG format
    * figure0008.svg

INSERT INTO demonstrations (teoId,proverId,code,dateSubmission,bibref,userId) VALUES ('GEO0008','2',' point O 25.80 48.30 point A 95.20 55.00 point B 120.10 91.60 point C 44.50 112.70 point O_1 62.40 56.80 line o1b O_1 B line oc O C line oa O A line o1c O_1 C line ob O B line o1a O_1 A intersec A_1 o1b oc intersec B_1 oa o1c line bb1 B B_1 line aa1 A A_1 intersec C_1 ob o1a intersec I bb1 aa1 line cc1i C I prove { collinear C C_1 I } ','2008/01/09', '','gpreda1 ')
The Proof's code 0008 is correct.

Processing the XML file, please wait
/usr/local/bin/gclc proof0008.code proofCode0008.xml -xml > proof0008.errors
Warning: fread() [function.fread]: Length parameter must be greater than 0 in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 497

INSERT INTO theorems (teoId,userId,category,description,shortDescription,teoName,dateSubmission) VALUES ('GEO0009','gpreda1 ','Geometry','\\begin{geothm} Let $C$ and $F$ be any points on the respective sides $AE$ and $BD$ of a parallelogram $ABCD$. Let $M$ and $N$ denote the points of intersection of $CD$ and $FA$ and of $EF$ and $BC$. Let the line $MN$ meet $DA$ at $P$ and $EB$ at $Q$. Then $AP \\cong QB$. \\end{geothm}',' ', ' Example 46 ','2008/01/09')

INSERT INTO bibtheorem (teoId,bibrefId) VALUES ('GEO0009','chou88')

INSERT INTO figures (teoId,drawerId,code,dateSubmission,bibref,userId) VALUES ('GEO0009','3',' dim 130 100 point A 20 20 point E 80 20 point B 95 70 point C 35 20 point F 65 70 line ae A E parallel bd B ae line be B E parallel ad A be intersec D bd ad line cd C D line af A F intersec M cd af line ef E F line bc B C intersec N ef bc line mn M N intersec P mn ad intersec Q mn be line pq P Q cmark_b A cmark_b E cmark_t B cmark_t D cmark_b C cmark_t F cmark_rb M cmark_rb N cmark_lt P cmark_rb Q drawsegment A E drawsegment E B drawsegment B D drawsegment D A drawdashsegment D C drawdashsegment A F drawdashsegment E F drawdashsegment C B drawline pq ','2008/01/09','chou88', 'gpreda1 ')
gclc figure0009.code figure0009.pic > figure0009.errors
Warning: fread() [function.fread]: Length parameter must be greater than 0 in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 328
Figura 64

    * Figure
    * figure0009.jpg
    * Description of the construction in natural language
    * figure0009.xml
    * Figure in SVG format
    * figure0009.svg

INSERT INTO demonstrations (teoId,proverId,code,dateSubmission,bibref,userId) VALUES ('GEO0009','2',' point A 20 20 point E 80 20 point B 95 70 point C 35 20 point F 65 70 line ae A E parallel bd B ae line be B E parallel ad A be intersec D bd ad line cd C D line af A F intersec M cd af line ef E F line bc B C intersec N ef bc line mn M N intersec P mn ad intersec Q mn be line pq P Q prove { equal { sratio A P Q B } { 1 } } ','2008/01/09', '','gpreda1 ')
The Proof's code 0009 is correct.

Processing the XML file, please wait
/usr/local/bin/gclc proof0009.code proofCode0009.xml -xml > proof0009.errors
Warning: fread() [function.fread]: Length parameter must be greater than 0 in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 497

INSERT INTO theorems (teoId,userId,category,description,shortDescription,teoName,dateSubmission) VALUES ('GEO0010','gpreda1 ','Geometry','\\begin{geothm} Prove that the line joining the point of intersection of the extensions of the nonparallel sides of a trapezoid to the point of intersection of its diagonals bisects the base of the trapezoid. \\end{geothm}',' ', ' Example 49 ','2008/01/09')

INSERT INTO bibtheorem (teoId,bibrefId) VALUES ('GEO0010','chou88')

INSERT INTO figures (teoId,drawerId,code,dateSubmission,bibref,userId) VALUES ('GEO0010','3',' dim 130 80 point A 20 20 point B 110 20 point C 90 50 point D 55 50 line bc B C line ad A D line cd C D line ab A B line ac A C line bd B D intersec F ad bc intersec E ac bd line ef E F intersec G ab ef cmark_b A cmark_b B cmark_rt C cmark_lt D cmark_rb E cmark_rt F cmark_b G drawsegment A F drawsegment B F drawsegment G F drawsegment A B drawsegment C D drawsegment A C drawsegment B D ','2008/01/09','chou88', 'gpreda1 ')
gclc figure0010.code figure0010.pic > figure0010.errors
Warning: fread() [function.fread]: Length parameter must be greater than 0 in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 328
Figura 72

    * Figure
    * figure0010.jpg
    * Description of the construction in natural language
    * figure0010.xml
    * Figure in SVG format
    * figure0010.svg

INSERT INTO demonstrations (teoId,proverId,code,dateSubmission,bibref,userId) VALUES ('GEO0010','2',' point A 20 20 point B 110 20 point C 90 50 point D 55 50 line bc B C line ad A D line cd C D line ab A B line ac A C line bd B D intersec F ad bc intersec E ac bd line ef E F intersec G ab ef prove { equal { sratio A G G B } { 1 } } ','2008/01/09', '','gpreda1 ')
The Proof's code 0010 is correct.

Processing the XML file, please wait
/usr/local/bin/gclc proof0010.code proofCode0010.xml -xml > proof0010.errors
Warning: fread() [function.fread]: Length parameter must be greater than 0 in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 497

INSERT INTO theorems (teoId,userId,category,description,shortDescription,teoName,dateSubmission) VALUES ('GEO0011','gpreda1 ','Geometry','\\begin{geothm} Show that triangle altitudes are concurrent. \\end{geothm}',' ', ' theorems\\thm_0070_Altitude.gcl ','2008/01/09')

INSERT INTO bibtheorem (teoId,bibrefId) VALUES ('GEO0010','chou88')

INSERT INTO figures (teoId,drawerId,code,dateSubmission,bibref,userId) VALUES ('GEO0011','3',' dim 100 85 point A 20 20 point B 80 20 point C 60 70 line bc B C line ab A B line ac A C foot A_1 A bc foot B_1 B ac foot C_1 C ab line ha A A_1 line hb B B_1 line hc C C_1 intersec H hc hb cmark_b A cmark_b B cmark_t C cmark_rt A_1 cmark_l B_1 cmark_b C_1 cmark_lb H drawsegment A B drawsegment A C drawsegment B C drawdashsegment B B_1 drawdashsegment A A_1 drawdashsegment C C_1 ','2008/01/09','', 'gpreda1 ')
gclc figure0011.code figure0011.pic > figure0011.errors
Warning: fread() [function.fread]: Length parameter must be greater than 0 in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 328
Figura 80

    * Figure
    * figure0011.jpg
    * Description of the construction in natural language
    * figure0011.xml
    * Figure in SVG format
    * figure0011.svg

INSERT INTO demonstrations (teoId,proverId,code,dateSubmission,bibref,userId) VALUES ('GEO0011','2',' point A 20 20 point B 80 20 point C 60 70 line bc B C line ab A B line ac A C foot A_1 A bc foot B_1 B ac foot C_1 C ab line ha A A_1 line hb B B_1 line hc C C_1 intersec H hc hb prove { collinear A H A_1 } ','2008/01/09', '','gpreda1 ')
The Proof's code 0011 is correct.

Processing the XML file, please wait
/usr/local/bin/gclc proof0011.code proofCode0011.xml -xml > proof0011.errors
Warning: fread() [function.fread]: Length parameter must be greater than 0 in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 497

INSERT INTO theorems (teoId,userId,category,description,shortDescription,teoName,dateSubmission) VALUES ('GEO0012','gpreda1 ','Geometry','\\begin{geothm} Let $l$ be a line passing through the vertex of $M$ of a parallelogram $MNPQ$ and intersecting the lines $NP$, $PQ$, $NQ$ in points $R$, $S$, $T$. Show that $1/MR + 1/MS = 1/MT$. \\end{geothm}',' ', ' Example 56 ','2008/01/09')

INSERT INTO bibtheorem (teoId,bibrefId) VALUES ('GEO0012','chou88')

INSERT INTO figures (teoId,drawerId,code,dateSubmission,bibref,userId) VALUES ('GEO0012','3',' dim 130 60 point M 20 20 point N 70 20 point P 85 45 line mn M N line np N P parallel pq P mn parallel mq M np intersec Q pq mq point S 120 45 line ms M S line nq N Q intersec T ms nq intersec R np ms cmark_b M cmark_b N cmark_b S cmark_b Q cmark_b T cmark_b R cmark_b P drawsegment M N drawsegment Q S drawsegment M Q drawsegment N P drawsegment M S drawsegment M Q drawsegment N Q ','2008/01/09','chou88', 'gpreda1 ')
gclc figure0012.code figure0012.pic > figure0012.errors
Warning: fread() [function.fread]: Length parameter must be greater than 0 in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 328
Figura 88

    * Figure
    * figure0012.jpg
    * Description of the construction in natural language
    * figure0012.xml
    * Figure in SVG format
    * figure0012.svg

INSERT INTO demonstrations (teoId,proverId,code,dateSubmission,bibref,userId) VALUES ('GEO0012','2',' point M 20 20 point N 70 20 point P 85 45 line mn M N line np N P parallel pq P mn parallel mq M np intersec Q pq mq point S 120 45 line ms M S line nq N Q intersec T ms nq intersec R np ms prove { equal { sum { sratio M T M R } { sratio M T M S } } { 1 } } } ','2008/01/09', '','gpreda1 ')
Syntax error: Unrecognized definition or command. (Line: 15, position: 69) There are errors in the proof's 0012 code.

INSERT INTO theorems (teoId,userId,category,description,shortDescription,teoName,dateSubmission) VALUES ('GEO0013','gpreda1 ','Geometry','\\begin{geothm} Let $A_1$, $B_1$, $C_1$ be points on the sides $BC$, $CA$, $AB$ of a triangle $ABC$ such that $BA_1/BC = CB_1/CA_1 = AC_1/AB = 1/3$. Show that the area of the triangle determined by lines $AA_1$, $BB_1$ and $CC_1$ is one seventh of the area of triangle $ABC$. \\end{geothm}',' ', ' Example 58 ','2008/01/09')

INSERT INTO bibtheorem (teoId,bibrefId) VALUES ('GEO0013','chou88')

INSERT INTO figures (teoId,drawerId,code,dateSubmission,bibref,userId) VALUES ('GEO0013','3',' dim 130 100 point A 20 20 point B 90 20 towards C_1 A B 0.333333333 point C 70 80 towards A_1 B C 0.333333333 towards B_1 C A 0.333333333 line aa1 A A_1 line bb1 B B_1 line cc1 C C_1 intersec A_2 bb1 cc1 intersec B_2 aa1 cc1 intersec C_2 aa1 bb1 cmark_b A cmark_b B cmark_b C_1 cmark_r C cmark_r A_1 cmark_lt B_1 cmark_b C_2 cmark_rb B_2 cmark_r A_2 drawsegment A B drawsegment A C drawsegment C B drawsegment C C_1 drawsegment A A_1 drawsegment B B_1 ','2008/01/09','chou88', 'gpreda1 ')
gclc figure0013.code figure0013.pic > figure0013.errors
Warning: fread() [function.fread]: Length parameter must be greater than 0 in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 328
Figura 96

    * Figure
    * figure0013.jpg
    * Description of the construction in natural language
    * figure0013.xml
    * Figure in SVG format
    * figure0013.svg

INSERT INTO demonstrations (teoId,proverId,code,dateSubmission,bibref,userId) VALUES ('GEO0013','2',' point A 20 20 point B 90 20 towards C_1 A B 0.333333333 point C 70 80 towards A_1 B C 0.333333333 towards B_1 C A 0.333333333 line aa1 A A_1 line bb1 B B_1 line cc1 C C_1 intersec A_2 bb1 cc1 intersec B_2 aa1 cc1 intersec C_2 aa1 bb1 prove { equal { signed_area3 A B C } { mult { 7 } { signed_area3 A_2 B_2 C_2 } } } ','2008/01/09', '','gpreda1 ')
The Proof's code 0013 is correct.

Processing the XML file, please wait
/usr/local/bin/gclc proof0013.code proofCode0013.xml -xml > proof0013.errors
Warning: fread() [function.fread]: Length parameter must be greater than 0 in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 497

INSERT INTO theorems (teoId,userId,category,description,shortDescription,teoName,dateSubmission) VALUES ('GEO0014','gpreda1 ','Geometry','\\begin{geothm} Show that median $CM$ divides triangle $ABC$ into two triangles of the same area. \\end{geothm}',' ', ' Triangle Area ','2008/01/09')

INSERT INTO bibtheorem (teoId,bibrefId) VALUES ('GEO0013','chou88')

INSERT INTO figures (teoId,drawerId,code,dateSubmission,bibref,userId) VALUES ('GEO0014','3',' dim 100 70 point A 20 20 point B 80 20 point C 65 45 midpoint M A B cmark_b A cmark_b B cmark_t C cmark_b M drawsegment A B drawsegment B C drawsegment A C drawsegment C M ','2008/01/09','', 'gpreda1 ')
gclc figure0014.code figure0014.pic > figure0014.errors
Warning: fread() [function.fread]: Length parameter must be greater than 0 in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 328
Figura 104

    * Figure
    * figure0014.jpg
    * Description of the construction in natural language
    * figure0014.xml
    * Figure in SVG format
    * figure0014.svg

INSERT INTO demonstrations (teoId,proverId,code,dateSubmission,bibref,userId) VALUES ('GEO0014','2',' point A 20 20 point B 80 20 point C 65 45 midpoint M A B prove { equal { signed_area3 A M C } { signed_area3 M B C } } ','2008/01/09', '','gpreda1 ')
The Proof's code 0014 is correct.

Processing the XML file, please wait
/usr/local/bin/gclc proof0014.code proofCode0014.xml -xml > proof0014.errors
Warning: fread() [function.fread]: Length parameter must be greater than 0 in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 497

INSERT INTO theorems (teoId,userId,category,description,shortDescription,teoName,dateSubmission) VALUES ('GEO0015','gpreda1 ','Geometry','\\begin{geothm} Let $M$, $N$, $P$ be points on the sides $AB$, $BC$ and $AC$ of a triangle $ABC$. Show that if $M_1$, $N_1$ and $P_1$ are points on sides $AC$, $BA$ and $BC$ of a triangle $ABC$ such that $MM_1 \\parallel BC$, $NN_1 \\parallel CA$ and $PP_1 \\parallel AB$, then triangles $MNP$ and $M_1N_1P_1$ have equal areas. \\end{geothm}',' ', ' Example 55 ','2008/01/09')

INSERT INTO bibtheorem (teoId,bibrefId) VALUES ('GEO0015','chou88')

INSERT INTO figures (teoId,drawerId,code,dateSubmission,bibref,userId) VALUES ('GEO0015','3',' dim 130 110 point A 20 20 point B 110 20 point C 80 90 point M 88 20 line ab A B line ac A C line bc B C point N 97.62 48.88 point P 36.68 39.46 parallel pp1 P ab parallel nn1 N ac parallel mm1 M bc intersec P_1 pp1 bc intersec M_1 mm1 ac intersec N_1 nn1 ab cmark_b A cmark_b B cmark_t C cmark_rt N cmark_b M cmark_lt P cmark_rt P_1 cmark_b N_1 cmark_lt M_1 drawsegment A B drawsegment A C drawsegment C B drawsegment P P_1 drawsegment M M_1 drawsegment N N_1 drawdashsegment M N drawdashsegment M P drawdashsegment P N drawdashsegment M_1 N_1 drawdashsegment M_1 P_1 drawdashsegment P_1 N_1 ','2008/01/09','chou88', 'gpreda1 ')
gclc figure0015.code figure0015.pic > figure0015.errors
Warning: fread() [function.fread]: Length parameter must be greater than 0 in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 328
Figura 112

    * Figure
    * figure0015.jpg
    * Description of the construction in natural language
    * figure0015.xml
    * Figure in SVG format
    * figure0015.svg

INSERT INTO demonstrations (teoId,proverId,code,dateSubmission,bibref,userId) VALUES ('GEO0015','2',' point A 20 20 point B 110 20 point C 80 90 point M 88 20 line ab A B line ac A C line bc B C online N B C online P A C parallel pp1 P ab parallel nn1 N ac parallel mm1 M bc intersec P_1 pp1 bc intersec M_1 mm1 ac intersec N_1 nn1 ab prove { equal { signed_area3 M N P } { signed_area3 M_1 N_1 P_1 } } ','2008/01/09', '','gpreda1 ')
The Proof's code 0015 is correct.

Processing the XML file, please wait
/usr/local/bin/gclc proof0015.code proofCode0015.xml -xml > proof0015.errors
Warning: fread() [function.fread]: Length parameter must be greater than 0 in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 497

INSERT INTO theorems (teoId,userId,category,description,shortDescription,teoName,dateSubmission) VALUES ('GEO0016','gpreda1 ','Geometry','\\begin{geothm} Let $A_1$, $B_1$, $C_1$, $D_1$ be points on the sides $CD$, $DA$, $AB$, $BC$ of a parallelogram $ABCD$ such that $CA_1/CD = DB_1/DA = AC_1/AB = BD_1/BC = 1/3$. Show that the area of the quadrilateral formed by the lines $AA_1$, $BB_1$, $CC_1$, $DD_1$ is one thirteenth of the area of parallelogram $ABCD$. \\end{geothm}',' ', ' Example 57 ','2008/01/09')

INSERT INTO bibtheorem (teoId,bibrefId) VALUES ('GEO0016','chou88')

INSERT INTO figures (teoId,drawerId,code,dateSubmission,bibref,userId) VALUES ('GEO0016','3',' dim 130 100 point A 20 20 point B 90 20 point C 110 80 line ab A B line bc B C parallel ad A bc parallel cd C ab intersec D ad cd towards C_1 A B 0.333333333 towards D_1 B C 0.333333333 towards A_1 C D 0.333333333 towards B_1 D A 0.333333333 line aa1 A A_1 line bb1 B B_1 line cc1 C C_1 line dd1 D D_1 intersec A_2 aa1 bb1 intersec B_2 bb1 cc1 intersec C_2 dd1 cc1 intersec D_2 aa1 dd1 cmark_b A cmark_b B cmark_b C_1 cmark_t C cmark_t A_1 cmark_lt B_1 cmark_b C_2 cmark_b B_2 cmark_b A_2 cmark_t D cmark_b D_2 cmark_r D_1 drawsegment A B drawsegment B C drawsegment C D drawsegment A D drawsegment C C_1 drawsegment A A_1 drawsegment B B_1 drawsegment D D_1 ','2008/01/09','chou88', 'gpreda1 ')
gclc figure0016.code figure0016.pic > figure0016.errors
Warning: fread() [function.fread]: Length parameter must be greater than 0 in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 328
Figura 120

    * Figure
    * figure0016.jpg
    * Description of the construction in natural language
    * figure0016.xml
    * Figure in SVG format
    * figure0016.svg

INSERT INTO demonstrations (teoId,proverId,code,dateSubmission,bibref,userId) VALUES ('GEO0016','2',' point A 20 20 point B 90 20 point C 110 80 line ab A B line bc B C parallel ad A bc parallel cd C ab intersec D ad cd towards C_1 A B 0.333333333 towards D_1 B C 0.333333333 towards A_1 C D 0.333333333 towards B_1 D A 0.333333333 line aa1 A A_1 line bb1 B B_1 line cc1 C C_1 line dd1 D D_1 intersec A_2 aa1 bb1 intersec B_2 bb1 cc1 intersec C_2 dd1 cc1 intersec D_2 aa1 dd1 prove { equal { signed_area4 A B C D } { mult { 13 } { signed_area4 A_2 B_2 C_2 D_2 } } } ','2008/01/09', '','gpreda1 ')
The Proof's code 0016 is correct.

Processing the XML file, please wait
/usr/local/bin/gclc proof0016.code proofCode0016.xml -xml > proof0016.errors
Warning: fread() [function.fread]: Length parameter must be greater than 0 in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 497

INSERT INTO theorems (teoId,userId,category,description,shortDescription,teoName,dateSubmission) VALUES ('GEO0017','gpreda1 ','Geometry','\\begin{geothm} Two doubly perspective triangles are in fact triply perspective. \\end{geothm}',' ', ' Example 59 ','2008/01/09')

INSERT INTO bibtheorem (teoId,bibrefId) VALUES ('GEO0017','chou88')

INSERT INTO figures (teoId,drawerId,code,dateSubmission,bibref,userId) VALUES ('GEO0017','3',' dim 130 100 point O 20 20 point A 70 20 point B 40.40 60.70 point C 73.20 52.50 point O_1 57.10 64.00 line co1 C O_1 line ao A O line ao1 A O_1 line bo B O line bo1 B O_1 line co C O intersec A_1 co1 ao intersec B_1 ao1 bo intersec C_1 bo1 co line ba1 B A_1 line ac1 A C_1 intersec O_2 ba1 ac1 cmark_b O cmark_b A cmark_l B cmark_r B_1 cmark_lt O_1 cmark_b C cmark_l O_2 cmark_rb C_1 cmark_b A_1 drawsegment O B_1 drawsegment O A_1 drawsegment O C_1 drawsegment A B_1 drawsegment B C_1 drawsegment A C_1 drawsegment B A_1 drawsegment O_1 A_1 line b1co2 B_1 C drawdashline b1co2 ','2008/01/09','chou88', 'gpreda1 ')
gclc figure0017.code figure0017.pic > figure0017.errors
Warning: fread() [function.fread]: Length parameter must be greater than 0 in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 328
Figura 128

    * Figure
    * figure0017.jpg
    * Description of the construction in natural language
    * figure0017.xml
    * Figure in SVG format
    * figure0017.svg

INSERT INTO demonstrations (teoId,proverId,code,dateSubmission,bibref,userId) VALUES ('GEO0017','2',' point O 20 20 point A 70 20 point B 40.40 60.70 point C 73.20 52.50 point O_1 57.10 64.00 line co1 C O_1 line ao A O line ao1 A O_1 line bo B O line bo1 B O_1 line co C O intersec A_1 co1 ao intersec B_1 ao1 bo intersec C_1 bo1 co line ba1 B A_1 line ac1 A C_1 intersec O_2 ba1 ac1 prove { collinear C B_1 O_2 } ','2008/01/09', '','gpreda1 ')
The Proof's code 0017 is correct.

Processing the XML file, please wait
/usr/local/bin/gclc proof0017.code proofCode0017.xml -xml > proof0017.errors
Warning: fread() [function.fread]: Length parameter must be greater than 0 in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 497

INSERT INTO theorems (teoId,userId,category,description,shortDescription,teoName,dateSubmission) VALUES ('GEO0018','gpreda1 ','Geometry','\\begin{geothm} The diagonals of a parallelogram and those of its inscribed parallelogram are concurrent. \\end{geothm}',' ', ' Example 69 ','2008/01/09')

INSERT INTO bibtheorem (teoId,bibrefId) VALUES ('GEO0018','chou88')

INSERT INTO figures (teoId,drawerId,code,dateSubmission,bibref,userId) VALUES ('GEO0018','3',' dim 130 100 point A 20 20 point B 90 20 point C 110 70 line ab A B line bc B C parallel cd C ab parallel ad A bc intersec D cd ad midpoint A_1 A B midpoint B_1 B C midpoint C_1 C D midpoint D_1 D A line ac A C line bd B D intersec O ac bd cmark_b A cmark_b B cmark_b A_1 cmark_t C cmark_t D cmark_t C_1 cmark_r B_1 cmark_l D_1 cmark_b O drawsegment A B drawsegment B C drawsegment C D drawsegment D A drawsegment A_1 B_1 drawsegment B_1 C_1 drawsegment C_1 D_1 drawsegment D_1 A_1 drawdashsegment A C drawdashsegment B D drawdashsegment A_1 C_1 drawdashsegment B_1 D_1 ','2008/01/09','chou88', 'gpreda1 ')
gclc figure0018.code figure0018.pic > figure0018.errors
Warning: fread() [function.fread]: Length parameter must be greater than 0 in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 328
Figura 136

    * Figure
    * figure0018.jpg
    * Description of the construction in natural language
    * figure0018.xml
    * Figure in SVG format
    * figure0018.svg

INSERT INTO demonstrations (teoId,proverId,code,dateSubmission,bibref,userId) VALUES ('GEO0018','2',' point A 20 20 point B 90 20 point C 110 70 line ab A B line bc B C parallel cd C ab parallel ad A bc intersec D cd ad midpoint A_1 A B midpoint B_1 B C midpoint C_1 C D midpoint D_1 D A line ac A C line bd B D intersec O ac bd prove { collinear A_1 C_1 O } prove { collinear D_1 B_1 O } ','2008/01/09', '','gpreda1 ')
The Proof's code 0018 is correct.

Processing the XML file, please wait
/usr/local/bin/gclc proof0018.code proofCode0018.xml -xml > proof0018.errors
Warning: fread() [function.fread]: Length parameter must be greater than 0 in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 497

INSERT INTO theorems (teoId,userId,category,description,shortDescription,teoName,dateSubmission) VALUES ('GEO0019','gpreda1 ','Geometry','\\begin{geothm} Given four points $A$, $B$, $C$ and $D$, points of intersections are formed: $L = AB \\cap CD$, $K = AC \\cap BC$, $F = KL \\cap BD$ and $G = KL \\cap AC$. Show that segment $KL$ is harmonically divided by the points $F$ and $G$, ie: $\\frac{\\overline{LK}}{\\overline{KF}} = \\frac{\\overline{GL}}{\\overline{GF}}$. \\end{geothm}',' ', ' Harmonic Points 2 ','2008/01/09')

INSERT INTO bibtheorem (teoId,bibrefId) VALUES ('GEO0018','chou88')

INSERT INTO figures (teoId,drawerId,code,dateSubmission,bibref,userId) VALUES ('GEO0019','3',' dim 130 50 point A 30 32 point B 40 40 point C 48 28 point D 40 25 cmark_lt A cmark_t B cmark_rt C cmark_lb D line AB A B line CD C D intersec L AB CD cmark_b L line AD A D line BC B C intersec K AD BC cmark_b K line BD B D line KL K L intersec F BD KL cmark_b F line AC A C intersec G AC KL cmark_b G drawsegment B L drawsegment C L drawsegment A K drawsegment B K drawsegment B F drawsegment A G line lkfg L K drawdashline lkfg ','2008/01/09','', 'gpreda1 ')
gclc figure0019.code figure0019.pic > figure0019.errors
Warning: fread() [function.fread]: Length parameter must be greater than 0 in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 328
Figura 144

    * Figure
    * figure0019.jpg
    * Description of the construction in natural language
    * figure0019.xml
    * Figure in SVG format
    * figure0019.svg

INSERT INTO demonstrations (teoId,proverId,code,dateSubmission,bibref,userId) VALUES ('GEO0019','2',' point A 30 32 point B 40 40 point C 48 28 point D 40 25 line AB A B line CD C D intersec L AB CD line AD A D line BC B C intersec K AD BC line BD B D line KL K L intersec F BD KL line AC A C intersec G AC KL line lkfg L K prove { harmonic L K F G } ','2008/01/09', '','gpreda1 ')
The Proof's code 0019 is correct.

Processing the XML file, please wait
/usr/local/bin/gclc proof0019.code proofCode0019.xml -xml > proof0019.errors
Warning: fread() [function.fread]: Length parameter must be greater than 0 in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 497

INSERT INTO theorems (teoId,userId,category,description,shortDescription,teoName,dateSubmission) VALUES ('GEO0020','gpreda1 ','Geometry','\\begin{geothm} Let $D$ be a point on the circumscribed cirle $(O)$ of triangle $ABC$. From $D$, three perpendiculars are drawn to the three sides $BC$, $CA$ and $AB$ of triangle $ABC$. Let $E$, $F$ and $G$ be the three feet respectively. Show that $E$, $F$ and $G$ are collinear. \\end{geothm}',' ', ' Simson s Theorem ','2008/01/09')

INSERT INTO bibtheorem (teoId,bibrefId) VALUES ('GEO0018','chou88')

INSERT INTO figures (teoId,drawerId,code,dateSubmission,bibref,userId) VALUES ('GEO0020','3',' dim 100 100 point A 20 50 point O 55 50 circle k O A point B 79.50 25.40 point C 49.50 84.50 point D 30.80 24.70 line ab A B line bc B C line ac A C foot E D bc foot F D ac foot G D ab cmark_l A cmark_b B cmark_t C cmark_b D cmark_t O cmark_t E cmark_t F cmark_t G drawsegment A B drawsegment F C drawsegment C B drawcircle k drawdashsegment E D drawdashsegment F D drawdashsegment G D line efg E F drawdashline efg ','2008/01/09','', 'gpreda1 ')
gclc figure0020.code figure0020.pic > figure0020.errors
Warning: fread() [function.fread]: Length parameter must be greater than 0 in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 328
Figura 152

    * Figure
    * figure0020.jpg
    * Description of the construction in natural language
    * figure0020.xml
    * Figure in SVG format
    * figure0020.svg

INSERT INTO demonstrations (teoId,proverId,code,dateSubmission,bibref,userId) VALUES ('GEO0020','2',' point A 20 50 point O 55 50 circle k O A oncircle B O A oncircle C O A oncircle D O A line ab A B line bc B C line ac A C foot E D bc foot F D ac foot G D ab line efg E F prove { collinear E F G } ','2008/01/09', '','gpreda1 ')
The Proof's code 0020 is correct.

Processing the XML file, please wait
/usr/local/bin/gclc proof0020.code proofCode0020.xml -xml > proof0020.errors
Warning: fread() [function.fread]: Length parameter must be greater than 0 in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 497

INSERT INTO theorems (teoId,userId,category,description,shortDescription,teoName,dateSubmission) VALUES ('GEO0021','gpreda1 ','Geometry','\\begin{geothm} The cross ratio of four points on a circles with respect to any points on the circle is constant. \\end{geothm}',' ', ' Example 77 ','2008/01/09')

INSERT INTO bibtheorem (teoId,bibrefId) VALUES ('GEO0021','chou88')

INSERT INTO figures (teoId,drawerId,code,dateSubmission,bibref,userId) VALUES ('GEO0021','3',' dim 130 100 point A 30 30 point B 100 30 point C 90 80 med m1 A B med m2 B C intersec O m1 m2 circle k O A point D 41.60 81.20 point P 46.10 14.20 point Q 84.90 14.70 line ab A B line pd P D line pc P C line qd Q D line qc Q C intersec F pd ab intersec G pc ab intersec F_1 qd ab intersec G_1 qc ab cmark_b A cmark_b B cmark_rt C cmark_lt D cmark_lb P cmark_rb Q cmark_r O cmark_lb F cmark_rb G cmark_lb F_1 cmark_rb G_1 drawsegment A B drawsegment A D drawsegment A C drawsegment B D drawsegment B C drawsegment P D drawsegment P C drawsegment Q D drawsegment Q C drawcircle k ','2008/01/09','chou88', 'gpreda1 ')
gclc figure0021.code figure0021.pic > figure0021.errors
Warning: fread() [function.fread]: Length parameter must be greater than 0 in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 328
Figura 160

    * Figure
    * figure0021.jpg
    * Description of the construction in natural language
    * figure0021.xml
    * Figure in SVG format
    * figure0021.svg

INSERT INTO demonstrations (teoId,proverId,code,dateSubmission,bibref,userId) VALUES ('GEO0021','2',' point A 30 30 point B 100 30 point C 90 80 med m1 A B med m2 B C intersec O m1 m2 circle k O A oncircle D O A oncircle P O A oncircle Q O A line pd P D line pc P C line qd Q D line qc Q C line ab A B intersec F pd ab intersec G pc ab intersec F_1 qd ab intersec G_1 qc ab prove { equal { mult { sratio G A G B } { sratio F B F A } } { mult { sratio G_1 A G_1 B } { sratio F_1 B F_1 A } } } ','2008/01/09', '','gpreda1 ')
The Proof's code 0021 is correct.

Processing the XML file, please wait
/usr/local/bin/gclc proof0021.code proofCode0021.xml -xml > proof0021.errors
Warning: fread() [function.fread]: Length parameter must be greater than 0 in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 497

INSERT INTO theorems (teoId,userId,category,description,shortDescription,teoName,dateSubmission) VALUES ('GEO0022','gpreda1 ','Geometry','\\begin{geothm} In triangle $ABC$, let $F$ the midpoint of the side $BC$, $D$ and $E$ the feet of the altitudes on $AB$ and $BC$, respectively. $FG$ is perpendicular to $DE$ at $G$. Show that $G$ is the midpoint of $DE$. \\end{geothm}',' ', ' Example 82 ','2008/01/09')

INSERT INTO bibtheorem (teoId,bibrefId) VALUES ('GEO0022','chou88')

INSERT INTO figures (teoId,drawerId,code,dateSubmission,bibref,userId) VALUES ('GEO0022','3',' dim 110 100 point A 20 20 point B 90 20 point C 70 70 midpoint F A B line ab A B line ac A C line bc B C foot P A bc foot Q B ac line pq P Q foot G F pq cmark_b A cmark_b B cmark_b F cmark_t C cmark_r P cmark_l Q cmark_t G drawsegment A B drawsegment C B drawsegment A C drawsegment A P drawsegment Q B drawsegment P Q drawsegment F G ','2008/01/09','chou88', 'gpreda1 ')
gclc figure0022.code figure0022.pic > figure0022.errors
Warning: fread() [function.fread]: Length parameter must be greater than 0 in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 328
Figura 168

    * Figure
    * figure0022.jpg
    * Description of the construction in natural language
    * figure0022.xml
    * Figure in SVG format
    * figure0022.svg

INSERT INTO demonstrations (teoId,proverId,code,dateSubmission,bibref,userId) VALUES ('GEO0022','2',' point A 20 20 point B 90 20 point C 70 70 midpoint F A B line ab A B line ac A C line bc B C foot P A bc foot Q B ac line pq P Q foot G F pq prove { equal { sratio Q G G P } { 1 } } ','2008/01/09', '','gpreda1 ')
The Proof's code 0022 is correct.

Processing the XML file, please wait
/usr/local/bin/gclc proof0022.code proofCode0022.xml -xml > proof0022.errors
Warning: fread() [function.fread]: Length parameter must be greater than 0 in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 497

INSERT INTO theorems (teoId,userId,category,description,shortDescription,teoName,dateSubmission) VALUES ('GEO0023','gpreda1 ','Geometry','\\begin{geothm} Let $P$ and $Q$ be two points on side $BC$ and $AD$ of a parallelogram such that $PQ \\parallel AB$; $M = AP \\cap BQ$, $N = DP \\cap QC$. Show that $MN \\parallel AD$ and $MN = AD/2$. \\end{geothm}',' ', ' Example 85 ','2008/01/09')

INSERT INTO bibtheorem (teoId,bibrefId) VALUES ('GEO0023','chou88')

INSERT INTO figures (teoId,drawerId,code,dateSubmission,bibref,userId) VALUES ('GEO0023','3',' dim 130 100 point A 20 20 point B 80 20 point C 110 70 line ab A B line bc B C parallel ad A bc parallel cd C ab intersec D ad cd point P 85.45 29.09 parallel pq P ab intersec Q pq ad line pd P D line qc Q C intersec N pd qc line pa P A line qb Q B intersec M pa qb cmark_b M cmark_b A cmark_t N cmark_b B cmark_t C cmark_t D cmark_r P cmark_l Q drawsegment P D drawsegment P A drawsegment Q C drawsegment B Q drawsegment P Q drawsegment A B drawsegment A D drawsegment C B drawsegment C D drawdashsegment M N ','2008/01/09','chou88', 'gpreda1 ')
gclc figure0023.code figure0023.pic > figure0023.errors
Warning: fread() [function.fread]: Length parameter must be greater than 0 in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 328
Figura 176

    * Figure
    * figure0023.jpg
    * Description of the construction in natural language
    * figure0023.xml
    * Figure in SVG format
    * figure0023.svg

INSERT INTO demonstrations (teoId,proverId,code,dateSubmission,bibref,userId) VALUES ('GEO0023','2',' point A 20 20 point B 80 20 point C 110 70 line ab A B line bc B C parallel ad A bc parallel cd C ab intersec D ad cd online P B C parallel pq P ab intersec Q pq ad line pd P D line qc Q C intersec N pd qc line pa P A line qb Q B intersec M pa qb prove { equal { sratio A D M N } { 2 } } ','2008/01/09', '','gpreda1 ')
The Proof's code 0023 is correct.

Processing the XML file, please wait
/usr/local/bin/gclc proof0023.code proofCode0023.xml -xml > proof0023.errors
Warning: fread() [function.fread]: Length parameter must be greater than 0 in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 497

INSERT INTO theorems (teoId,userId,category,description,shortDescription,teoName,dateSubmission) VALUES ('GEO0024','gpreda1 ','Geometry','\\begin{geothm} Show that the sum of distances of a point on the base of an isosceles triangle to its two sides is equal to the altitudes on the sides. \\end{geothm}',' ', ' Example 88 ','2008/01/09')

INSERT INTO bibtheorem (teoId,bibrefId) VALUES ('GEO0024','chou88')

INSERT INTO figures (teoId,drawerId,code,dateSubmission,bibref,userId) VALUES ('GEO0024','3',' dim 110 80 point A 20 20 point B 90 20 point C 33.17 60.88 point D 23.73 31.58 line ab A B line bc B C foot E D ab foot F D bc foot H C ab cmark_b A cmark_b B cmark_t C cmark_l D cmark_b H cmark_b E cmark_rt F drawsegment A B drawsegment A C drawsegment C B drawsegment C H drawsegment D E drawsegment D F ','2008/01/09','chou88', 'gpreda1 ')
gclc figure0024.code figure0024.pic > figure0024.errors
Warning: fread() [function.fread]: Length parameter must be greater than 0 in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 328
Figura 184

    * Figure
    * figure0024.jpg
    * Description of the construction in natural language
    * figure0024.xml
    * Figure in SVG format
    * figure0024.svg

INSERT INTO demonstrations (teoId,proverId,code,dateSubmission,bibref,userId) VALUES ('GEO0024','2',' point A 20 20 point B 90 20 oncircle C B A online D A C line ab A B line bc B C foot E D ab foot F D bc foot H C ab prove { alg_sum_zero3 { segment D E } { segment D F } { segment C H } } ','2008/01/09', '','gpreda1 ')
The Proof's code 0024 is correct.

Processing the XML file, please wait
/usr/local/bin/gclc proof0024.code proofCode0024.xml -xml > proof0024.errors
Warning: fopen(proof0024.xml.bz2) [function.fopen]: failed to open stream: No such file or directory in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 508

Warning: filesize() [function.filesize]: stat failed for proof0024.xml.bz2 in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 509

Warning: fread(): supplied argument is not a valid stream resource in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 509

Warning: fclose(): supplied argument is not a valid stream resource in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 511

INSERT INTO theorems (teoId,userId,category,description,shortDescription,teoName,dateSubmission) VALUES ('GEO0025','gpreda1 ','Geometry','\\begin{geothm} Given quadrilateral $ABCD$, let $M_1$ and $M_2$ be midpoints of diagonals $AC$ and $BD$, and let $O$ be point on line $M_1M_2$. Show that the sum of areas of triangles $ABO$ and $CDO$ equals the half of the area of quadrilateral $ABCD$. \\end{geothm}',' ', ' Leon Anne s Theorem ','2008/01/09')

INSERT INTO bibtheorem (teoId,bibrefId) VALUES ('GEO0024','chou88')

INSERT INTO figures (teoId,drawerId,code,dateSubmission,bibref,userId) VALUES ('GEO0025','3',' dim 110 110 point A 20 20 point B 90 20 point C 75 85 point D 40 65 midpoint M_1 A C midpoint M_2 B D line m12 M_1 M_2 point O 31.05 61.90 line ac A C line bd B D drawline ac drawline bd drawdashline m12 cmark_b M_1 cmark_b M_2 cmark_t O cmark_b A cmark_b B cmark_t C cmark_t D drawsegment A B drawsegment C B drawsegment C D drawsegment A D ','2008/01/09','', 'gpreda1 ')
gclc figure0025.code figure0025.pic > figure0025.errors
Warning: fread() [function.fread]: Length parameter must be greater than 0 in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 328
Figura 192

    * Figure
    * figure0025.jpg
    * Description of the construction in natural language
    * figure0025.xml
    * Figure in SVG format
    * figure0025.svg

INSERT INTO demonstrations (teoId,proverId,code,dateSubmission,bibref,userId) VALUES ('GEO0025','2',' point A 20 20 point B 90 20 point C 75 85 point D 40 65 midpoint M_1 A C midpoint M_2 B D line m12 M_1 M_2 online O M_1 M_2 line ac A C line bd B D prove { equal { mult { 2 } { sum { signed_area3 A B O } { signed_area3 C D O } } } { signed_area4 A B C D } } } ','2008/01/09', '','gpreda1 ')
Syntax error: Unrecognized definition or command. (Line: 12, position: 111) There are errors in the proof's 0025 code.

INSERT INTO theorems (teoId,userId,category,description,shortDescription,teoName,dateSubmission) VALUES ('GEO0026','gpreda1 ','Geometry','\\begin{geothm} Of the three lines joining the vertices of an equilateral triangle to a point on its circumcircle, one is equal to the sum of the other two. \\end{geothm}',' ', ' Example 119 ','2008/01/09')

INSERT INTO bibtheorem (teoId,bibrefId) VALUES ('GEO0026','chou88')

INSERT INTO figures (teoId,drawerId,code,dateSubmission,bibref,userId) VALUES ('GEO0026','3',' dim 110 100 point A 20 30 point B 90 30 circle k A B med mc A B intersec2 C C1 k mc med mb A C intersec O mc mb circle k1 O A point P 75.80 84.86 cmark_lb A cmark_rb B cmark_rt P cmark_b O cmark_t C drawsegment A B drawsegment A C drawsegment C B drawdashsegment P A drawdashsegment P B drawdashsegment P C drawcircle k1 ','2008/01/09','chou88', 'gpreda1 ')
gclc figure0026.code figure0026.pic > figure0026.errors
Warning: fread() [function.fread]: Length parameter must be greater than 0 in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 328
Figura 200

    * Figure
    * figure0026.jpg
    * Description of the construction in natural language
    * figure0026.xml
    * Figure in SVG format
    * figure0026.svg

INSERT INTO demonstrations (teoId,proverId,code,dateSubmission,bibref,userId) VALUES ('GEO0026','2',' point A 20 30 point B 90 30 circle k A B med mc A B intersec2 C C1 k mc med mb A C intersec O mc mb circle k1 O A oncircle P O A prove { alg_sum_zero3 { segment P A } { segment P B } { segment P C } } ','2008/01/09', '','gpreda1 ')
The Proof's code 0026 is correct.

Processing the XML file, please wait
/usr/local/bin/gclc proof0026.code proofCode0026.xml -xml > proof0026.errors
Warning: fopen(proof0026.xml.bz2) [function.fopen]: failed to open stream: No such file or directory in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 508

Warning: filesize() [function.filesize]: stat failed for proof0026.xml.bz2 in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 509

Warning: fread(): supplied argument is not a valid stream resource in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 509

Warning: fclose(): supplied argument is not a valid stream resource in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 511

INSERT INTO theorems (teoId,userId,category,description,shortDescription,teoName,dateSubmission) VALUES ('GEO0027','gpreda1 ','Geometry','\\begin{geothm} Three parallel lines drawn through the vertices of a triangle $ABC$ meet the respective opposite sides in the points $X$, $Y$, $Z$. Show that area ratio $P_{XYZ} : P_{ABC} = 2 : 1$. \\end{geothm}',' ', ' Example 120 ','2008/01/09')

INSERT INTO bibtheorem (teoId,bibrefId) VALUES ('GEO0027','chou88')

INSERT INTO figures (teoId,drawerId,code,dateSubmission,bibref,userId) VALUES ('GEO0027','3',' dim 110 100 point A 50 50 point B 90 50 point C 75 80 point X 82 66 line ab A B line bc B C line ac A C line ax A X parallel cz C ax parallel by B ax intersec Y by ac intersec Z cz ab cmark_t Z cmark_b Y cmark_rt X cmark_b A cmark_b B cmark_t C drawsegment Z B drawsegment Y C drawsegment Z X drawsegment A X drawsegment Y Z drawsegment B C drawsegment C Z drawsegment Y B drawsegment X Y ','2008/01/09','chou88', 'gpreda1 ')
gclc figure0027.code figure0027.pic > figure0027.errors
Warning: fread() [function.fread]: Length parameter must be greater than 0 in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 328
Figura 208

    * Figure
    * figure0027.jpg
    * Description of the construction in natural language
    * figure0027.xml
    * Figure in SVG format
    * figure0027.svg

INSERT INTO demonstrations (teoId,proverId,code,dateSubmission,bibref,userId) VALUES ('GEO0027','2',' point A 50 50 point B 90 50 point C 75 80 online X B C line ab A B line bc B C line ac A C line ax A X parallel cz C ax parallel by B ax intersec Y by ac intersec Z cz ab prove { equal { mult { 2 } { signed_area3 B A C } } { signed_area3 X Y Z } } ','2008/01/09', '','gpreda1 ')
The Proof's code 0027 is correct.

Processing the XML file, please wait
/usr/local/bin/gclc proof0027.code proofCode0027.xml -xml > proof0027.errors
Warning: fread() [function.fread]: Length parameter must be greater than 0 in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 497

INSERT INTO theorems (teoId,userId,category,description,shortDescription,teoName,dateSubmission) VALUES ('GEO0028','gpreda1 ','Geometry','\\begin{geothm} Let $PT$ and $PB$ be two tangents to a circle, $AB$ the diameter through $B$, and $TH$ the perpendicular from $T$ to $AB$. Then $AP$ bisects $TH$. \\end{geothm}',' ', ' Example 37 ','2008/01/09')

INSERT INTO bibtheorem (teoId,bibrefId) VALUES ('GEO0028','chou88')

INSERT INTO figures (teoId,drawerId,code,dateSubmission,bibref,userId) VALUES ('GEO0028','3',' dim 130 110 point A 30 50 point B 90 50 midpoint O A B circle k O A point T 69.10 78.59 line ab A B perp bp B ab line ot O T perp tp T ot intersec P bp tp foot H T ab line th T H line ap A P intersec I th ap cmark_lb A cmark_b H cmark_b O cmark_rb B cmark_r P cmark_t T cmark_rb I drawsegment A B drawsegment A P drawsegment T H drawsegment T O drawsegment P B drawsegment P T drawcircle k ','2008/01/09','chou88', 'gpreda1 ')
gclc figure0028.code figure0028.pic > figure0028.errors
Warning: fread() [function.fread]: Length parameter must be greater than 0 in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 328
Figura 216

    * Figure
    * figure0028.jpg
    * Description of the construction in natural language
    * figure0028.xml
    * Figure in SVG format
    * figure0028.svg

INSERT INTO demonstrations (teoId,proverId,code,dateSubmission,bibref,userId) VALUES ('GEO0028','2',' point A 30 50 point B 90 50 midpoint O A B circle k O A oncircle T O A line ab A B perp bp B ab line ot O T perp tp T ot intersec P bp tp foot H T ab line th T H line ap A P intersec I th ap prove { equal { sratio T I I H } { 1 } } ','2008/01/09', '','gpreda1 ')
The Proof's code 0028 is correct.

Processing the XML file, please wait
/usr/local/bin/gclc proof0028.code proofCode0028.xml -xml > proof0028.errors
Warning: fread() [function.fread]: Length parameter must be greater than 0 in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 497

INSERT INTO theorems (teoId,userId,category,description,shortDescription,teoName,dateSubmission) VALUES ('GEO0029','gpreda1 ','Geometry','\\begin{geothm} If a quadrangle $ABCD$ has its opposite sides $AD$ and $BC$ (extended) meeting at $W$, while $X$ and $Y$ are the midpoints of the diagonals $AC$ and $BD$, then $(WXY) = 1/4(ABCD)$. \\end{geothm}',' ', ' Example 42 ','2008/01/09')

INSERT INTO bibtheorem (teoId,bibrefId) VALUES ('GEO0029','chou88')

INSERT INTO figures (teoId,drawerId,code,dateSubmission,bibref,userId) VALUES ('GEO0029','3',' dim 110 90 point A 20 20 point B 60 20 point C 50 50 point D 35 65 line ab A B line cd C D intersec W ab cd midpoint X A C midpoint Y B D cmark_b X cmark_b Y cmark_b W cmark_b A cmark_b B cmark_t C cmark_t D drawsegment A W drawsegment C B drawsegment D W drawsegment A D drawdashsegment B D drawdashsegment C A drawsegment X Y drawsegment X W drawsegment Y W ','2008/01/09','chou88', 'gpreda1 ')
gclc figure0029.code figure0029.pic > figure0029.errors
Warning: fread() [function.fread]: Length parameter must be greater than 0 in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 328
Figura 224

    * Figure
    * figure0029.jpg
    * Description of the construction in natural language
    * figure0029.xml
    * Figure in SVG format
    * figure0029.svg

INSERT INTO demonstrations (teoId,proverId,code,dateSubmission,bibref,userId) VALUES ('GEO0029','2',' point A 20 20 point B 60 20 point C 50 50 point D 35 65 line ab A B line cd C D intersec W ab cd midpoint X A C midpoint Y B D prove { equal { mult { 4 } { signed_area3 X W Y } } { signed_area4 A B C D } } ','2008/01/09', '','gpreda1 ')
The Proof's code 0029 is correct.

Processing the XML file, please wait
/usr/local/bin/gclc proof0029.code proofCode0029.xml -xml > proof0029.errors
Warning: fread() [function.fread]: Length parameter must be greater than 0 in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 497

INSERT INTO theorems (teoId,userId,category,description,shortDescription,teoName,dateSubmission) VALUES ('GEO0030','gpreda1 ','Geometry','\\begin{geothm} If lines $A_1B_1$, $A_2B_2$ and $A_3B_3$ are concurrent, show that intersections $A_1A_2 \\cap B_1B_2$, $A_1A_3 \\cap B_1B_3$ and $A_2A_3 \\cap B_2B_3$ are collinear. \\end{geothm}',' ', ' Desargues theorem ','2008/01/09')

INSERT INTO bibtheorem (teoId,bibrefId) VALUES ('GEO0029','chou88')

INSERT INTO figures (teoId,drawerId,code,dateSubmission,bibref,userId) VALUES ('GEO0030','3',' dim 110 90 point S 20 30 point A_2 36.60 30 point B_2 53.00 30 point A_1 27.20 24.70 point B_1 38.40 16.434 point A_3 42.20 41.10 point B_3 56 48 line a12 A_1 A_2 line a13 A_1 A_3 line a23 A_2 A_3 line b12 B_1 B_2 line b13 B_1 B_3 line b23 B_2 B_3 intersec P a12 b12 intersec Q a13 b13 intersec R a23 b23 line pqr P Q drawdashline pqr drawline a12 drawline a13 drawline a23 drawline b12 drawline b13 drawline b23 cmark_t P cmark_l Q cmark_l R cmark_b A_1 cmark_rb A_2 cmark_rb A_3 cmark_b B_1 cmark_rb B_2 cmark_rb B_3 cmark_b S line sa1 S A_1 line sa2 S A_2 line sa3 S A_3 drawline sa1 drawline sa2 drawline sa3 ','2008/01/09','', 'gpreda1 ')
gclc figure0030.code figure0030.pic > figure0030.errors
Warning: fread() [function.fread]: Length parameter must be greater than 0 in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 328
Figura 232

    * Figure
    * figure0030.jpg
    * Description of the construction in natural language
    * figure0030.xml
    * Figure in SVG format
    * figure0030.svg

INSERT INTO demonstrations (teoId,proverId,code,dateSubmission,bibref,userId) VALUES ('GEO0030','2',' point S 20 30 point A_2 36.60 30 point B_2 53.00 30 point A_1 27.20 24.70 online B_1 S A_1 point A_3 42.20 41.10 online B_3 S A_3 line a12 A_1 A_2 line a13 A_1 A_3 line a23 A_2 A_3 line b12 B_1 B_2 line b13 B_1 B_3 line b23 B_2 B_3 intersec P a12 b12 intersec Q a13 b13 intersec R a23 b23 prove { collinear P Q R } ','2008/01/09', '','gpreda1 ')
The Proof's code 0030 is correct.

Processing the XML file, please wait
/usr/local/bin/gclc proof0030.code proofCode0030.xml -xml > proof0030.errors
Warning: fread() [function.fread]: Length parameter must be greater than 0 in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 497

INSERT INTO theorems (teoId,userId,category,description,shortDescription,teoName,dateSubmission) VALUES ('GEO0031','gpreda1 ','Geometry','\\begin{geothm} Given triangle $ABC$, let $A_1$, $B_1$ and $C_1$ endpoints of triangle altitudes. From each of points $A_1$, $B_1$ and $C_1$ feet are drawn upon triangle sides, those are: $A_2$, $A_3$, $B_2$, $B_3$, $C_2$ and $C_3$. Show that these six points lie on a circle. \\end{geothm}',' ', ' Six Points Circle ','2008/01/09')

INSERT INTO bibtheorem (teoId,bibrefId) VALUES ('GEO0029','chou88')

INSERT INTO figures (teoId,drawerId,code,dateSubmission,bibref,userId) VALUES ('GEO0031','3',' dim 130 100 point A 20 20 point B 90 20 point C 70 70 line ac A C line ab A B line bc B C foot A_1 A bc foot B_1 B ac foot C_1 C ab foot C_2 C_1 bc foot C_3 C_1 ac foot A_2 A_1 ac foot A_3 A_1 ab foot B_2 B_1 bc foot B_3 B_1 ab med p B_3 A_3 med q B_3 C_3 intersec O p q circle k O B_3 cmark_b A cmark_b B cmark_t C cmark_r A_1 cmark_l B_1 cmark_b C_1 cmark_b A_3 cmark_b B_3 cmark_l C_3 cmark_lt A_2 cmark_r C_2 cmark_rt B_2 drawsegment A B drawsegment A C drawsegment C B drawdashsegment A A_1 drawdashsegment B B_1 drawdashsegment C C_1 drawdashsegment C_1 C_2 drawdashsegment C_1 C_3 drawdashsegment A_1 A_2 drawdashsegment A_1 A_3 drawdashsegment B_1 B_2 drawdashsegment B_1 B_3 drawcircle k ','2008/01/09','', 'gpreda1 ')
gclc figure0031.code figure0031.pic > figure0031.errors
Warning: fread() [function.fread]: Length parameter must be greater than 0 in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 328
Figura 240

    * Figure
    * figure0031.jpg
    * Description of the construction in natural language
    * figure0031.xml
    * Figure in SVG format
    * figure0031.svg

INSERT INTO demonstrations (teoId,proverId,code,dateSubmission,bibref,userId) VALUES ('GEO0031','2',' point A 20 20 point B 90 20 point C 70 70 line ac A C line ab A B line bc B C foot A_1 A bc foot B_1 B ac foot C_1 C ab foot C_2 C_1 bc foot C_3 C_1 ac foot A_2 A_1 ac foot A_3 A_1 ab foot B_2 B_1 bc foot B_3 B_1 ab med p B_3 A_3 med q B_3 C_3 intersec O p q prove { equal { segment O C_2 } { segment O B_3 } } prove { equal { segment O A_2 } { segment O B_3 } } ','2008/01/09', '','gpreda1 ')
The Proof's code 0031 is correct.

Processing the XML file, please wait
/usr/local/bin/gclc proof0031.code proofCode0031.xml -xml > proof0031.errors
Warning: fopen(proof0031.xml.bz2) [function.fopen]: failed to open stream: No such file or directory in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 508

Warning: filesize() [function.filesize]: stat failed for proof0031.xml.bz2 in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 509

Warning: fread(): supplied argument is not a valid stream resource in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 509

Warning: fclose(): supplied argument is not a valid stream resource in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 511

INSERT INTO theorems (teoId,userId,category,description,shortDescription,teoName,dateSubmission) VALUES ('GEO0032','gpreda1 ','Geometry','\\begin{geothm} If quadrilateral $ABCD$ is inscribed in circle, show that angles $\\angle ACB$ and $\\angle ADB$ are equal. \\end{geothm}',' ', ' Quadrilateral Inscribed in Circle ','2008/01/09')

INSERT INTO bibtheorem (teoId,bibrefId) VALUES ('GEO0029','chou88')

INSERT INTO figures (teoId,drawerId,code,dateSubmission,bibref,userId) VALUES ('GEO0032','3',' dim 110 90 point A 40 20 point B 70 20 point X 56 45 line ax A X med m A B intersec O ax m circle k O A drawcircle k point C 33.76 61.42 point D 69.32 67.30 drawsegment C A drawsegment C B drawsegment D A drawsegment D B cmark_lt C cmark_rt D cmark_lb A cmark_rb B drawsegment A B ','2008/01/09','', 'gpreda1 ')
gclc figure0032.code figure0032.pic > figure0032.errors
Warning: fread() [function.fread]: Length parameter must be greater than 0 in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 328
Figura 248

    * Figure
    * figure0032.jpg
    * Description of the construction in natural language
    * figure0032.xml
    * Figure in SVG format
    * figure0032.svg

INSERT INTO demonstrations (teoId,proverId,code,dateSubmission,bibref,userId) VALUES ('GEO0032','2',' point A 40 20 point B 70 20 point X 56 45 line ax A X med m A B intersec O ax m circle k O A oncircle C O A oncircle D O A prove { equal { angle A C B } { angle A D B } } ','2008/01/09', '','gpreda1 ')
The Proof's code 0032 is correct.

Processing the XML file, please wait
/usr/local/bin/gclc proof0032.code proofCode0032.xml -xml > proof0032.errors
Warning: fopen(proof0032.xml.bz2) [function.fopen]: failed to open stream: No such file or directory in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 508

Warning: filesize() [function.filesize]: stat failed for proof0032.xml.bz2 in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 509

Warning: fread(): supplied argument is not a valid stream resource in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 509

Warning: fclose(): supplied argument is not a valid stream resource in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 511

INSERT INTO theorems (teoId,userId,category,description,shortDescription,teoName,dateSubmission) VALUES ('GEO0033','gpreda1 ','Geometry','\\begin{geothm} Let $H$ and $O$ be the orthocenter and circumcenter of triangle $ABC$. Show $\\angle HAC = | \\angle B - \\angle C |$. \\end{geothm}',' ', ' Example 30 ','2008/01/09')

INSERT INTO bibtheorem (teoId,bibrefId) VALUES ('GEO0033','chou88')

INSERT INTO figures (teoId,drawerId,code,dateSubmission,bibref,userId) VALUES ('GEO0033','3',' dim 130 110 point C 20 30 point B 110 30 point A 90 95 line ab A B line ac A C line bc B C foot D A bc foot B_1 B ac line ha A D line hb B B_1 intersec H ha hb med ma A B med mb A C intersec O ma mb circle k O A cmark_lb C cmark_rb B cmark_rt A cmark_r H cmark_l O cmark_b D drawsegment A B drawsegment A C drawsegment B C drawsegment A D drawcircle k drawsegment O A drawsegment H A ','2008/01/09','chou88', 'gpreda1 ')
gclc figure0033.code figure0033.pic > figure0033.errors
Warning: fread() [function.fread]: Length parameter must be greater than 0 in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 328
Figura 256

    * Figure
    * figure0033.jpg
    * Description of the construction in natural language
    * figure0033.xml
    * Figure in SVG format
    * figure0033.svg

INSERT INTO demonstrations (teoId,proverId,code,dateSubmission,bibref,userId) VALUES ('GEO0033','2',' point C 20 30 point B 110 30 point A 90 95 line ab A B line ac A C line bc B C foot D A bc med ma A B med mb A C intersec O ma mb prove { equal { sum { angle O A D } { mult { mult { mult { angle A B C } { angle O A D } } { angle A C B } } { -1 } } } { sum { angle A B C } { angle A C B } } } ','2008/01/09', '','gpreda1 ')
The Proof's code 0033 is correct.

Processing the XML file, please wait
/usr/local/bin/gclc proof0033.code proofCode0033.xml -xml > proof0033.errors
Warning: fopen(proof0033.xml.bz2) [function.fopen]: failed to open stream: No such file or directory in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 508

Warning: filesize() [function.filesize]: stat failed for proof0033.xml.bz2 in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 509

Warning: fread(): supplied argument is not a valid stream resource in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 509

Warning: fclose(): supplied argument is not a valid stream resource in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 511

INSERT INTO theorems (teoId,userId,category,description,shortDescription,teoName,dateSubmission) VALUES ('GEO0034','gpreda1 ','Geometry','\\begin{geothm} Hexagon $ABCDEF$ is incsibed in a circle with center $O$. Show that three points at which pairs of opposite sides meet, lie on a straight line. \\end{geothm}',' ', ' Pascal s Theorem ','2008/01/09')

INSERT INTO bibtheorem (teoId,bibrefId) VALUES ('GEO0033','chou88')

INSERT INTO figures (teoId,drawerId,code,dateSubmission,bibref,userId) VALUES ('GEO0034','3',' dim 100 100 point A 20.50 51.40 point O 50 50 circle k O A point B 60.40 77.60 point C 72.30 69.20 point D 21.40 42.10 point E 51.30 20.60 point F 78.20 41.90 line ab A B line df D F line bc B C line fe F E line cd C D line ea E A drawdashline ab drawdashline df drawdashline bc drawdashline fe drawdashline cd drawdashline ea intersec P ab df intersec Q bc fe intersec S cd ea cmark_lt A cmark_t O cmark_t B cmark_t C cmark_lb D cmark_t E cmark_lt F cmark_t P cmark_t Q cmark_t S drawcircle k line pqs P Q drawline pqs ','2008/01/09','', 'gpreda1 ')
gclc figure0034.code figure0034.pic > figure0034.errors
Warning: fread() [function.fread]: Length parameter must be greater than 0 in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 328
Figura 264

    * Figure
    * figure0034.jpg
    * Description of the construction in natural language
    * figure0034.xml
    * Figure in SVG format
    * figure0034.svg

INSERT INTO demonstrations (teoId,proverId,code,dateSubmission,bibref,userId) VALUES ('GEO0034','2',' point A 20.50 51.40 point O 50 50 circle k O A oncircle B O A oncircle C O A oncircle D O A oncircle E O A oncircle F O A line ab A B line df D F line bc B C line fe F E line cd C D line ea E A intersec P ab df intersec Q bc fe intersec S cd ea line pqs P Q prove { collinear P Q S } ','2008/01/09', '','gpreda1 ')
The Proof's code 0034 is correct.

Processing the XML file, please wait
/usr/local/bin/gclc proof0034.code proofCode0034.xml -xml > proof0034.errors
Warning: fread() [function.fread]: Length parameter must be greater than 0 in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 497

INSERT INTO theorems (teoId,userId,category,description,shortDescription,teoName,dateSubmission) VALUES ('GEO0035','gpreda1 ','Geometry','\\begin{geothm} Let $ABC$ be a triangle with $\\angle B = 2\\angle C$, D the foot of the altitude on $CB$ and $M$ the midpoint of $B$ and $C$. Show that $AB = 2DM$. \\end{geothm}',' ', ' Example 86 ','2008/01/09')

INSERT INTO bibtheorem (teoId,bibrefId) VALUES ('GEO0035','chou88')

INSERT INTO figures (teoId,drawerId,code,dateSubmission,bibref,userId) VALUES ('GEO0035','3',' dim 110 80 point C 20 20 point B 90 20 line bc B C med m B C point A_1 80 60 line ab A_1 B intersec F ab m bis ca B C F intersec A ca ab intersec M bc m foot D A bc cmark_b C cmark_b B cmark_r A cmark_b M cmark_b D drawsegment B C drawsegment A C drawsegment B A drawsegment D A drawsegment M A ','2008/01/09','chou88', 'gpreda1 ')
gclc figure0035.code figure0035.pic > figure0035.errors
Warning: fread() [function.fread]: Length parameter must be greater than 0 in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 328
Figura 272

    * Figure
    * figure0035.jpg
    * Description of the construction in natural language
    * figure0035.xml
    * Figure in SVG format
    * figure0035.svg

INSERT INTO demonstrations (teoId,proverId,code,dateSubmission,bibref,userId) VALUES ('GEO0035','2',' point C 20 20 point B 90 20 line bc B C med m B C point A_1 80 60 line ab A_1 B intersec F ab m bis ca B C F intersec A ca ab intersec M bc m foot D A bc prove { equal { mult { 4 } { segment D M } } { segment A B } } ','2008/01/09', '','gpreda1 ')
The Proof's code 0035 is correct.

Processing the XML file, please wait
/usr/local/bin/gclc proof0035.code proofCode0035.xml -xml > proof0035.errors
Warning: fopen(proof0035.xml.bz2) [function.fopen]: failed to open stream: No such file or directory in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 508

Warning: filesize() [function.filesize]: stat failed for proof0035.xml.bz2 in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 509

Warning: fread(): supplied argument is not a valid stream resource in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 509

Warning: fclose(): supplied argument is not a valid stream resource in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 511

INSERT INTO theorems (teoId,userId,category,description,shortDescription,teoName,dateSubmission) VALUES ('GEO0036','gpreda1 ','Geometry','\\begin{geothm} Given a triangle $ABC$ and a point $X$, the sum of the distances of the line $XG$, where $G$ is the centroid of $ABC$, to the two vertices of the triangle situated on the same side of the line is equal to the distance of the line from the third vertex. \\end{geothm}',' ', ' Example 20 from \\cite{geothms} ','2008/01/09')

INSERT INTO bibtheorem (teoId,bibrefId) VALUES ('GEO0035','chou88')

INSERT INTO figures (teoId,drawerId,code,dateSubmission,bibref,userId) VALUES ('GEO0036','3',' dim 110 100 point A 20 20 point C 65 80 point T 55 45 towards A_1 A T 1.5 towards C_1 C T 1.5 line bc C A_1 line ab A C_1 intersec B ab bc point X 95 45 line gx T X foot D A gx foot E B gx foot F C gx cmark_t D cmark_t E cmark_b F cmark_lt T cmark_b A cmark_b B cmark_t C cmark_t X drawline gx drawsegment A B drawsegment A C drawsegment C B drawsegment A A_1 drawsegment C C_1 drawdashsegment A D drawdashsegment B E drawdashsegment C F ','2008/01/09','', 'gpreda1 ')
gclc figure0036.code figure0036.pic > figure0036.errors
Warning: fread() [function.fread]: Length parameter must be greater than 0 in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 328
Figura 280

    * Figure
    * figure0036.jpg
    * Description of the construction in natural language
    * figure0036.xml
    * Figure in SVG format
    * figure0036.svg

INSERT INTO demonstrations (teoId,proverId,code,dateSubmission,bibref,userId) VALUES ('GEO0036','2',' point A 20 20 point C 65 80 point T 55 45 towards A_1 A T 1.5 towards C_1 C T 1.5 line bc C A_1 line ab A C_1 intersec B ab bc point X 95 45 line gx T X foot D A gx foot E B gx foot F C gx prove { equal { sum { sum { sratio A D A D } { sratio B E A D } } { sratio C F A D } } { 0 } } ','2008/01/09', '','gpreda1 ')
The Proof's code 0036 is correct.

Processing the XML file, please wait
/usr/local/bin/gclc proof0036.code proofCode0036.xml -xml > proof0036.errors
Warning: fread() [function.fread]: Length parameter must be greater than 0 in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 497

INSERT INTO theorems (teoId,userId,category,description,shortDescription,teoName,dateSubmission) VALUES ('GEO0037','gpreda1 ','Geometry','\\begin{geothm} Given a parallelogram $ABCD$, a point $N$, obtained by the intersection of a line parallel to $BD$ passing through $C$, and a line perpendicular to $BD$ passing through $A$, then the point $Q$, which is given by the intersection of $BN$ and $CD$, is the midpoint of $PC$, where $P$ is the intersection of $CD$ and $AN$, \\end{geothm}',' ', ' Example 22 from \\cite{geothms} ','2008/01/09')

INSERT INTO bibtheorem (teoId,bibrefId) VALUES ('GEO0035','chou88')

INSERT INTO figures (teoId,drawerId,code,dateSubmission,bibref,userId) VALUES ('GEO0037','3',' dim 110 90 point A 20 20 point B 70 20 point C 85 60 line ab A B line bc B C parallel ad A bc parallel cd C ab intersec D ad cd line bd B D parallel cn C bd perp an A bd intersec N cn an line bn B N intersec P cd an intersec Q bn cd drawline cn drawline an drawsegment A N drawsegment B N drawsegment B D cmark_lt P cmark_lb Q cmark_t N cmark_b A cmark_b B cmark_t C cmark_t D drawsegment A B drawsegment C B drawsegment C D drawsegment A D ','2008/01/09','', 'gpreda1 ')
gclc figure0037.code figure0037.pic > figure0037.errors
Warning: fread() [function.fread]: Length parameter must be greater than 0 in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 328
Figura 288

    * Figure
    * figure0037.jpg
    * Description of the construction in natural language
    * figure0037.xml
    * Figure in SVG format
    * figure0037.svg

INSERT INTO demonstrations (teoId,proverId,code,dateSubmission,bibref,userId) VALUES ('GEO0037','2',' point A 20 20 point B 70 20 point C 85 60 line ab A B line bc B C parallel ad A bc parallel cd C ab intersec D ad cd line bd B D parallel cn C bd perp an A bd intersec N cn an line bn B N intersec P cd an intersec Q bn cd prove { equal { sratio P Q Q C } { 1 } } ','2008/01/09', '','gpreda1 ')
The Proof's code 0037 is correct.

Processing the XML file, please wait
/usr/local/bin/gclc proof0037.code proofCode0037.xml -xml > proof0037.errors
Warning: fread() [function.fread]: Length parameter must be greater than 0 in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 497

INSERT INTO theorems (teoId,userId,category,description,shortDescription,teoName,dateSubmission) VALUES ('GEO0038','gpreda1 ','Geometry','\\begin{geothm} Assume $S_1$, $S_2$, $S_3$ are the points of contact of the incircle of $ABC$: $S_1$ on side $AC$, etc. Denote the intersection of $BC$ and $S_1S_3$ as $P$, that of $AC$ and $S_2S_3$ as $Q$, and let $R$ be the intersection of $AB$ and $S_1S_2$. Then points $P$, $Q$, and $R$ are collinear. \\end{geothm}',' ', ' Nobbs Theorem ','2008/01/09')

INSERT INTO bibtheorem (teoId,bibrefId) VALUES ('GEO0035','chou88')

INSERT INTO figures (teoId,drawerId,code,dateSubmission,bibref,userId) VALUES ('GEO0038','3',' dim 130 130 point X 20 20 point Y 25 20 point S_3 65 20 point O 65 32 line ab X Y circle k O S_3 point S_1 75.90 36.70 point S_2 60.10 42.90 line os2 O S_2 line os1 O S_1 perp as1 S_1 os1 perp bs2 S_2 os2 intersec A ab as1 intersec B ab bs2 intersec C as1 bs2 line s13 S_1 S_3 intersec P s13 bs2 line s23 S_2 S_3 intersec Q s23 as1 line s12 S_1 S_2 intersec R s12 ab line pqr P Q drawcircle k drawline pqr drawdashline s23 drawdashline s13 drawdashline s12 drawdashsegment C P drawdashsegment C Q drawdashsegment A R cmark_b R cmark_rt Q cmark_r P cmark_t C cmark_b A cmark_b B cmark_l S_1 cmark_b S_2 cmark_rb S_3 drawsegment A C drawsegment A B drawsegment B C ','2008/01/09','', 'gpreda1 ')
gclc figure0038.code figure0038.pic > figure0038.errors
Warning: fread() [function.fread]: Length parameter must be greater than 0 in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 328
Figura 296

    * Figure
    * figure0038.jpg
    * Description of the construction in natural language
    * figure0038.xml
    * Figure in SVG format
    * figure0038.svg

INSERT INTO demonstrations (teoId,proverId,code,dateSubmission,bibref,userId) VALUES ('GEO0038','2',' point X 20 20 point Y 25 20 point S_3 65 20 point O 65 32 line ab X Y circle k O S_3 oncircle S_1 O S_3 oncircle S_2 O S_3 line os2 O S_2 line os1 O S_1 perp as1 S_1 os1 perp bs2 S_2 os2 intersec A ab as1 intersec B ab bs2 intersec C as1 bs2 line s13 S_1 S_3 intersec P s13 bs2 line s23 S_2 S_3 intersec Q s23 as1 line s12 S_1 S_2 intersec R s12 ab line pqr P Q prove { collinear P Q R } ','2008/01/09', '','gpreda1 ')
The Proof's code 0038 is correct.

Processing the XML file, please wait
/usr/local/bin/gclc proof0038.code proofCode0038.xml -xml > proof0038.errors
Warning: fread() [function.fread]: Length parameter must be greater than 0 in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 497

INSERT INTO theorems (teoId,userId,category,description,shortDescription,teoName,dateSubmission) VALUES ('GEO0039','gpreda1 ','Geometry','\\begin{geothm} Line $p$ intersects lines $AB$, $AC$ and $BC$ at points $F$, $E$ and $D$ respectively. Show that: \\end{geothm}',' ', ' Menelaus s Theorem ','2008/01/09')

INSERT INTO bibtheorem (teoId,bibrefId) VALUES ('GEO0035','chou88')

INSERT INTO figures (teoId,drawerId,code,dateSubmission,bibref,userId) VALUES ('GEO0039','3',' dim 100 80 point A 30 20 point B 60 20 point C 40 50 line c A B point D 53.33 30 point E 36.66 40 line p D E intersec F c p drawsegment A B drawsegment A C drawsegment B C drawline D E drawline A B cmark_b A cmark_b B cmark_t C cmark_rt D cmark_lt E cmark_rt F ','2008/01/09','', 'gpreda1 ')
gclc figure0039.code figure0039.pic > figure0039.errors
Warning: fread() [function.fread]: Length parameter must be greater than 0 in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 328
Figura 304

    * Figure
    * figure0039.jpg
    * Description of the construction in natural language
    * figure0039.xml
    * Figure in SVG format
    * figure0039.svg

INSERT INTO demonstrations (teoId,proverId,code,dateSubmission,bibref,userId) VALUES ('GEO0039','2',' point A 30 20 point B 60 20 point C 40 50 line c A B online D B C online E A C line p D E intersec F c p prove { equal { mult { mult { sratio A F F B } { sratio B D D C } } { sratio C E E A } } -1 } ','2008/01/09', '','gpreda1 ')
The Proof's code 0039 is correct.

Processing the XML file, please wait
/usr/local/bin/gclc proof0039.code proofCode0039.xml -xml > proof0039.errors
Warning: fread() [function.fread]: Length parameter must be greater than 0 in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 497

INSERT INTO theorems (teoId,userId,category,description,shortDescription,teoName,dateSubmission) VALUES ('GEO0040','gpreda1 ','Geometry','\\begin{geothm} The midpoints of the three diagonals of a complete quadrilateral are collinear. This line is called Gauss line. \\end{geothm}',' ', ' Gauss line ','2008/01/09')

INSERT INTO bibtheorem (teoId,bibrefId) VALUES ('GEO0035','chou88')

INSERT INTO figures (teoId,drawerId,code,dateSubmission,bibref,userId) VALUES ('GEO0040','3',' dim 90 80 point A_0 30 10 point A_1 70 10 point A_2 55 40 point A_3 35 25 line a12 A_1 A_2 line a03 A_0 A_3 line a01 A_0 A_1 line a23 A_2 A_3 intersec X a12 a03 intersec Y a01 a23 midpoint M_1 A_1 A_3 midpoint M_2 A_0 A_2 midpoint M_3 X Y cmark_b A_0 cmark_b A_1 cmark_rt A_2 cmark_l A_3 cmark_t X cmark_b Y cmark_b M_1 cmark_r M_2 cmark_rt M_3 drawsegment A_0 A_1 drawsegment A_0 A_2 drawsegment A_0 A_3 drawsegment A_1 A_2 drawsegment A_1 A_3 drawsegment A_2 A_3 drawdashsegment A_1 X drawdashsegment A_3 X drawdashsegment A_0 Y drawdashsegment A_2 Y drawline M_1 M_2 ','2008/01/09','', 'gpreda1 ')
gclc figure0040.code figure0040.pic > figure0040.errors
Warning: fread() [function.fread]: Length parameter must be greater than 0 in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 328
Figura 312

    * Figure
    * figure0040.jpg
    * Description of the construction in natural language
    * figure0040.xml
    * Figure in SVG format
    * figure0040.svg

INSERT INTO demonstrations (teoId,proverId,code,dateSubmission,bibref,userId) VALUES ('GEO0040','2',' point A_0 30 10 point A_1 70 10 point A_2 55 40 point A_3 35 25 line a12 A_1 A_2 line a03 A_0 A_3 line a01 A_0 A_1 line a23 A_2 A_3 intersec X a12 a03 intersec Y a01 a23 midpoint M_1 A_1 A_3 midpoint M_2 A_0 A_2 midpoint M_3 X Y prove { collinear M_1 M_2 M_3 } ','2008/01/09', '','gpreda1 ')
The Proof's code 0040 is correct.

Processing the XML file, please wait
/usr/local/bin/gclc proof0040.code proofCode0040.xml -xml > proof0040.errors
Warning: fread() [function.fread]: Length parameter must be greater than 0 in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 497

INSERT INTO theorems (teoId,userId,category,description,shortDescription,teoName,dateSubmission) VALUES ('GEO0041','gpreda1 ','Geometry','\\begin{geothm} A tranversal curs the sides $BC$, $CA$, $AB$ of triangle $ABC$ in $D$, $E$, $F$. $P$, $Q$, $R$ are the midpoints of $EF$, $FD$, $DE$ and $AP$, $BQ$, $CR$ intersec $BC$, $CA$, $AB$ in $X$, $Y$, $Z$. Show that $X$, $Y$, $Z$ are collinear. \\end{geothm}',' ', ' Example 25 ','2008/01/09')

INSERT INTO bibtheorem (teoId,bibrefId) VALUES ('GEO0041','chou88')

INSERT INTO figures (teoId,drawerId,code,dateSubmission,bibref,userId) VALUES ('GEO0041','3',' dim 150 110 point A 20 20 point B 70 20 point C 60 70 line ab A B line bc B C line ac A C point F 63 20 point D 66.06 39.70 line fd F D intersec E fd ac midpoint P E F midpoint Q F D midpoint R D E line ap A P line bq B Q line cr C R intersec X ap bc intersec Y bq ac intersec Z cr ab line xyz X Y drawdashline xyz cmark_lb X cmark_t Y cmark_b Z cmark_r P cmark_l Q cmark_r R cmark_t E cmark_b F cmark_r D cmark_b A cmark_b B cmark_t C drawsegment A P drawsegment B Y drawsegment C Z drawsegment A Z drawsegment C B drawsegment A E drawsegment F E ','2008/01/09','chou88', 'gpreda1 ')
gclc figure0041.code figure0041.pic > figure0041.errors
Warning: fread() [function.fread]: Length parameter must be greater than 0 in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 328
Figura 320

    * Figure
    * figure0041.jpg
    * Description of the construction in natural language
    * figure0041.xml
    * Figure in SVG format
    * figure0041.svg

INSERT INTO demonstrations (teoId,proverId,code,dateSubmission,bibref,userId) VALUES ('GEO0041','2',' point A 20 20 point B 70 20 point C 60 70 line ab A B line bc B C line ac A C online F A B online D B C line fd F D intersec E fd ac midpoint P E F midpoint Q F D midpoint R D E line ap A P line bq B Q line cr C R intersec X ap bc intersec Y bq ac intersec Z cr ab line xyz X Y prove { collinear X Y Z } ','2008/01/09', '','gpreda1 ')
The Proof's code 0041 is correct.

Processing the XML file, please wait
/usr/local/bin/gclc proof0041.code proofCode0041.xml -xml > proof0041.errors
Warning: fread() [function.fread]: Length parameter must be greater than 0 in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 497

INSERT INTO theorems (teoId,userId,category,description,shortDescription,teoName,dateSubmission) VALUES ('GEO0042','gpreda1 ','Geometry','\\begin{geothm} In a hexagon $AC_1BA_1CB_1$, $BB_1$, $C_1A$, $A_1C$ are concurrent and $CC_1$, $A_1B$, $B_1A$ are concurrent. Prove that $AA_1$, $B_1C$, $C_1B$ are also concurrent. \\end{geothm}',' ', ' Example 28 ','2008/01/09')

INSERT INTO bibtheorem (teoId,bibrefId) VALUES ('GEO0042','chou88')

INSERT INTO figures (teoId,drawerId,code,dateSubmission,bibref,userId) VALUES ('GEO0042','3',' dim 110 90 point A 30 20 point C_1 58 20 point B 20 37 point A_1 37 50 point C 60 35 line ac1 A C_1 line a1c A_1 C intersec O ac1 a1c line ba1 B A_1 line cc1 C C_1 intersec H ba1 cc1 line ah A H line bo B O intersec B_1 bo ah line cb1 C B_1 line bc1 B C_1 intersec I cb1 bc1 cmark_rb B_1 cmark_t H cmark_rb A cmark_b C_1 cmark_lb B cmark_lt A_1 cmark_rt C cmark_b O drawsegment B H drawsegment A H drawsegment C_1 H drawsegment A O drawsegment B O drawsegment A_1 O drawsegment A B drawsegment B C drawdashline C B_1 drawdashline B C_1 drawdashline A A_1 ','2008/01/09','chou88', 'gpreda1 ')
gclc figure0042.code figure0042.pic > figure0042.errors
Warning: fread() [function.fread]: Length parameter must be greater than 0 in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 328
Figura 328

    * Figure
    * figure0042.jpg
    * Description of the construction in natural language
    * figure0042.xml
    * Figure in SVG format
    * figure0042.svg

INSERT INTO demonstrations (teoId,proverId,code,dateSubmission,bibref,userId) VALUES ('GEO0042','2',' point A 30 20 point C_1 58 20 point B 20 37 point A_1 37 50 point C 60 35 line ac1 A C_1 line a1c A_1 C intersec O ac1 a1c line ba1 B A_1 line cc1 C C_1 intersec H ba1 cc1 line ah A H line bo B O intersec B_1 bo ah line cb1 C B_1 line bc1 B C_1 intersec I cb1 bc1 prove { collinear A A_1 I } ','2008/01/09', '','gpreda1 ')
The Proof's code 0042 is correct.

Processing the XML file, please wait
/usr/local/bin/gclc proof0042.code proofCode0042.xml -xml > proof0042.errors
Warning: fread() [function.fread]: Length parameter must be greater than 0 in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 497

INSERT INTO theorems (teoId,userId,category,description,shortDescription,teoName,dateSubmission) VALUES ('GEO0043','gpreda1 ','Geometry','\\begin{geothm} In a triangle $ABC$, let $p$ and $q$ be the radii of two circles through $A$, touching side $BC$ at $B$ and $C$, respectively. Then $pq = R^2$. \\end{geothm}',' ', ' Example 29 ','2008/01/09')

INSERT INTO bibtheorem (teoId,bibrefId) VALUES ('GEO0043','chou88')

INSERT INTO figures (teoId,drawerId,code,dateSubmission,bibref,userId) VALUES ('GEO0043','3',' dim 90 90 point B 20 20 point C 70 20 point A 55 60 med ma B C med mb A C intersec O ma mb line bc B C perp p B bc med mc A B intersec P p mc perp q C bc intersec Q mb q circle k1 Q A circle k2 P A drawcircle k1 drawcircle k2 cmark_t P cmark_t Q cmark_b B cmark_b C cmark_t A cmark_t O drawsegment P B drawsegment P A drawsegment Q C drawsegment Q A drawdashsegment O B drawdashsegment O C drawsegment A B drawsegment C B drawsegment A C ','2008/01/09','chou88', 'gpreda1 ')
gclc figure0043.code figure0043.pic > figure0043.errors
Warning: fread() [function.fread]: Length parameter must be greater than 0 in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 328
Figura 336

    * Figure
    * figure0043.jpg
    * Description of the construction in natural language
    * figure0043.xml
    * Figure in SVG format
    * figure0043.svg

INSERT INTO demonstrations (teoId,proverId,code,dateSubmission,bibref,userId) VALUES ('GEO0043','2',' point B 20 20 point C 70 20 point A 55 60 med ma B C med mb A C intersec O ma mb line bc B C perp p B bc med mc A B intersec P p mc perp q C bc intersec Q mb q prove { equal { mult { segment Q C } { segment P B } } { mult { segment O B } { segment O B } } } ','2008/01/09', '','gpreda1 ')
The Proof's code 0043 is correct.

Processing the XML file, please wait
/usr/local/bin/gclc proof0043.code proofCode0043.xml -xml > proof0043.errors
Warning: fopen(proof0043.xml.bz2) [function.fopen]: failed to open stream: No such file or directory in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 508

Warning: filesize() [function.filesize]: stat failed for proof0043.xml.bz2 in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 509

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INSERT INTO theorems (teoId,userId,category,description,shortDescription,teoName,dateSubmission) VALUES ('GEO0044','gpreda1 ','Geometry','\\begin{geothm} $OH^2 = 9R^2 - a^2 - b^2 - c^2$. \\end{geothm}',' ', ' Example 31 ','2008/01/09')

INSERT INTO bibtheorem (teoId,bibrefId) VALUES ('GEO0044','chou88')

INSERT INTO figures (teoId,drawerId,code,dateSubmission,bibref,userId) VALUES ('GEO0044','3',' dim 90 90 point A 20 20 point B 70 20 point C 55 70 med ma B C med mc A B intersec O ma mc line ab A B perp ch C ab line ac A C perp bh B ac intersec H ch bh intersec D ch ab circle k O A drawcircle k cmark_b O cmark_l H cmark_lb A cmark_rb B cmark_t C drawsegment C D drawsegment C O drawsegment A O drawsegment A B drawsegment A C drawsegment C B ','2008/01/09','chou88', 'gpreda1 ')
gclc figure0044.code figure0044.pic > figure0044.errors
Warning: fread() [function.fread]: Length parameter must be greater than 0 in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 328
Figura 344

    * Figure
    * figure0044.jpg
    * Description of the construction in natural language
    * figure0044.xml
    * Figure in SVG format
    * figure0044.svg

INSERT INTO demonstrations (teoId,proverId,code,dateSubmission,bibref,userId) VALUES ('GEO0044','2',' point A 20 20 point B 70 20 point C 55 70 med ma B C med mc A B intersec O ma mc line ab A B perp ch C ab line ac A C perp bh B ac intersec H ch bh prove { equal { mult { 9 } { segment O A } } { sum { segment O H } { sum { segment A B } { sum { segment A C } { segment B C } } } } } ','2008/01/09', '','gpreda1 ')
The Proof's code 0044 is correct.

Processing the XML file, please wait
/usr/local/bin/gclc proof0044.code proofCode0044.xml -xml > proof0044.errors
Warning: fopen(proof0044.xml.bz2) [function.fopen]: failed to open stream: No such file or directory in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 508

Warning: filesize() [function.filesize]: stat failed for proof0044.xml.bz2 in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 509

Warning: fread(): supplied argument is not a valid stream resource in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 509

Warning: fclose(): supplied argument is not a valid stream resource in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 511

INSERT INTO theorems (teoId,userId,category,description,shortDescription,teoName,dateSubmission) VALUES ('GEO0045','gpreda1 ','Geometry','\\begin{geothm} The sum of distances of a point inside an equilateral triangle or on one of its sides to the three triangle segments, equals the length of its altitude. \\end{geothm}',' ', ' Viviani s Theorem ','2008/01/09')

INSERT INTO bibtheorem (teoId,bibrefId) VALUES ('GEO0044','chou88')

INSERT INTO figures (teoId,drawerId,code,dateSubmission,bibref,userId) VALUES ('GEO0045','3',' dim 110 100 point A 20 20 point B 90 20 point P 65 40 circle k A B med p A B intersec2 C C1 k p line ab A B intersec D ab p line bc B C line ac A C foot G P ac foot F P bc foot E P ab foot H P p cmark_b D cmark_b A cmark_b B cmark_t C cmark_t P cmark_l H cmark_lt G cmark_rt F cmark_b E drawsegment A B drawsegment A C drawsegment C B drawsegment C D drawsegment P H drawsegment P G drawsegment P F drawsegment P E ','2008/01/09','', 'gpreda1 ')
gclc figure0045.code figure0045.pic > figure0045.errors
Warning: fread() [function.fread]: Length parameter must be greater than 0 in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 328
Figura 352

    * Figure
    * figure0045.jpg
    * Description of the construction in natural language
    * figure0045.xml
    * Figure in SVG format
    * figure0045.svg

INSERT INTO demonstrations (teoId,proverId,code,dateSubmission,bibref,userId) VALUES ('GEO0045','2',' point A 20 20 point B 90 20 point P 65 40 circle k A B med p A B intersec2 C C1 k p line ab A B intersec D ab p line bc B C line ac A C foot G P ac foot F P bc foot E P ab foot H P p prove { alg_sum_zero3 { segment C H } { segment P F } { segment P G } } ','2008/01/09', '','gpreda1 ')
The Proof's code 0045 is correct.

Processing the XML file, please wait
/usr/local/bin/gclc proof0045.code proofCode0045.xml -xml > proof0045.errors
Warning: fopen(proof0045.xml.bz2) [function.fopen]: failed to open stream: No such file or directory in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 508

Warning: filesize() [function.filesize]: stat failed for proof0045.xml.bz2 in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 509

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INSERT INTO theorems (teoId,userId,category,description,shortDescription,teoName,dateSubmission) VALUES ('GEO0046','gpreda1 ','Geometry','\\begin{geothm} Show that every triangle has incenter. \\end{geothm}',' ', ' Incenter Exists Theorem ','2008/01/09')

INSERT INTO bibtheorem (teoId,bibrefId) VALUES ('GEO0044','chou88')

INSERT INTO figures (teoId,drawerId,code,dateSubmission,bibref,userId) VALUES ('GEO0046','3',' dim 110 110 point A 20 20 point B 90 20 point C 70 90 bis sa B A C bis sc A C B bis sb C B A intersec S sa sb line ab A B intersec C1 sc ab cmark_rb S drawdashline sa drawdashline sb drawdashline sc cmark_b A cmark_b B cmark_lt C drawsegment A B drawsegment C B drawsegment A C ','2008/01/09','', 'gpreda1 ')
gclc figure0046.code figure0046.pic > figure0046.errors
Warning: fread() [function.fread]: Length parameter must be greater than 0 in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 328
Figura 360

    * Figure
    * figure0046.jpg
    * Description of the construction in natural language
    * figure0046.xml
    * Figure in SVG format
    * figure0046.svg

INSERT INTO demonstrations (teoId,proverId,code,dateSubmission,bibref,userId) VALUES ('GEO0046','2',' point A 20 20 point B 90 20 point C 70 90 bis sa B A C bis sc A C B bis sb C B A intersec S sa sb line ab A B prove { equal { angle A C S } { angle S C B } } ','2008/01/09', '','gpreda1 ')
The Proof's code 0046 is correct.

Processing the XML file, please wait
/usr/local/bin/gclc proof0046.code proofCode0046.xml -xml > proof0046.errors
Warning: fopen(proof0046.xml.bz2) [function.fopen]: failed to open stream: No such file or directory in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 508

Warning: filesize() [function.filesize]: stat failed for proof0046.xml.bz2 in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 509

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INSERT INTO theorems (teoId,userId,category,description,shortDescription,teoName,dateSubmission) VALUES ('GEO0047','gpreda1 ','Geometry','\\begin{geothm} The feet of the four perpendiculars dropped from a vertex of a triangle upon the four bisectors of the other two angles are collinear. \\end{geothm}',' ', ' Example 152 ','2008/01/09')

INSERT INTO bibtheorem (teoId,bibrefId) VALUES ('GEO0047','chou88')

INSERT INTO figures (teoId,drawerId,code,dateSubmission,bibref,userId) VALUES ('GEO0047','3',' dim 120 110 point A 30 30 point B 100 30 point C 50 88 bis s1 B A C bis s2 A B C perp s3 A s1 perp s4 B s2 foot P C s1 foot Q C s2 foot R C s3 foot S C s4 cmark_b A cmark_rb B cmark_t C cmark_b P cmark_lb Q cmark_lb R cmark_rb S line p P Q drawline p drawdashline s1 drawdashline s2 drawdashline s3 drawdashline s4 line a A B drawline a drawsegment A C drawsegment C B drawsegment C P drawsegment C Q drawsegment C R drawsegment C S ','2008/01/09','chou88', 'gpreda1 ')
gclc figure0047.code figure0047.pic > figure0047.errors
Warning: fread() [function.fread]: Length parameter must be greater than 0 in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 328
Figura 368

    * Figure
    * figure0047.jpg
    * Description of the construction in natural language
    * figure0047.xml
    * Figure in SVG format
    * figure0047.svg

INSERT INTO demonstrations (teoId,proverId,code,dateSubmission,bibref,userId) VALUES ('GEO0047','2',' point A 30 30 point B 100 30 point C 50 88 bis s1 B A C bis s2 A B C foot P C s1 foot Q C s2 line p P Q prove { parallel P Q A B } ','2008/01/09', '','gpreda1 ')
The Proof's code 0047 is correct.

Processing the XML file, please wait
/usr/local/bin/gclc proof0047.code proofCode0047.xml -xml > proof0047.errors
Warning: fopen(proof0047.xml.bz2) [function.fopen]: failed to open stream: No such file or directory in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 508

Warning: filesize() [function.filesize]: stat failed for proof0047.xml.bz2 in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 509

Warning: fread(): supplied argument is not a valid stream resource in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 509

Warning: fclose(): supplied argument is not a valid stream resource in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 511

INSERT INTO theorems (teoId,userId,category,description,shortDescription,teoName,dateSubmission) VALUES ('GEO0048','gpreda1 ','Geometry','\\begin{geothm} Isosceles right triangle $ABC$ with right angle at point $C$ is given. Let $E$ be a point on side $AC$ of a triangle. Let $D$ be the intersection of a line passing through $E$ parallel with line $AB$ and a line. $BC$. Let $p$ and $q$ be lines perpendicular with line $BE$ passing through points $D$ and $C$, and let $K$ and $L$ be intersections of lines $p$ and $q$ with hypotenuse $AB$. Show that $L$ is a midpoint of a segment $KA$. \\end{geothm}',' ', ' Isosceles Right Triangle Problem ','2008/01/09')

INSERT INTO bibtheorem (teoId,bibrefId) VALUES ('GEO0047','chou88')

INSERT INTO figures (teoId,drawerId,code,dateSubmission,bibref,userId) VALUES ('GEO0048','3',' dim 110 110 point C 20 20 point A 90 20 circle k C A line ac A C perp bc C ac intersec2 B B1 bc k point E 47 20 line ab A B line be B E parallel ed E ab intersec D ed bc perp cl C be perp dk D be intersec L cl ab intersec K dk ab cmark_rt K cmark_rt L cmark_b E cmark_l D cmark_t B cmark_b C cmark_b A drawdashsegment D E drawsegment E B drawsegment A C drawsegment A B drawsegment B C drawsegment D K drawsegment C L ','2008/01/09','', 'gpreda1 ')
gclc figure0048.code figure0048.pic > figure0048.errors
Warning: fread() [function.fread]: Length parameter must be greater than 0 in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 328
Figura 376

    * Figure
    * figure0048.jpg
    * Description of the construction in natural language
    * figure0048.xml
    * Figure in SVG format
    * figure0048.svg

INSERT INTO demonstrations (teoId,proverId,code,dateSubmission,bibref,userId) VALUES ('GEO0048','2',' point C 20 20 point A 90 20 circle k C A line ac A C perp bc C ac intersec2 B B1 bc k online E A C line ab A B line be B E parallel ed E ab intersec D ed bc perp cl C be perp dk D be intersec L cl ab intersec K dk ab prove { equal { sratio K L L A } { 1 } } ','2008/01/09', '','gpreda1 ')
The Proof's code 0048 is correct.

Processing the XML file, please wait
/usr/local/bin/gclc proof0048.code proofCode0048.xml -xml > proof0048.errors
Warning: fread() [function.fread]: Length parameter must be greater than 0 in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 497

INSERT INTO theorems (teoId,userId,category,description,shortDescription,teoName,dateSubmission) VALUES ('GEO0049','gpreda1 ','Geometry','\\begin{geothm} $P_1$, $P_2$, $P_3$ and $P_4$ are four points on circle $k$ with a center $O$. $M$ is the intersection of $P_1P_3$ and $P_2P_4$. Through $M$ draw a line $l$ perpendicular to $OM$, meeting $P_2P_3$ at $X$ and $P_1P_4$ at $Y$. Show that $MX \\cong MY$. \\end{geothm}',' ', ' Butterfly theorem ','2008/01/09')

INSERT INTO bibtheorem (teoId,bibrefId) VALUES ('GEO0047','chou88')

INSERT INTO figures (teoId,drawerId,code,dateSubmission,bibref,userId) VALUES ('GEO0049','3',' dim 100 100 point P_1 32 40 point O 62 40 circle k O P_1 point P_2 35.80 25.50 point P_3 62.80 69.90 point P_4 77.80 14.80 line p1p3 P_1 P_3 line p2p4 P_2 P_4 line p1p4 P_1 P_4 line p2p3 P_2 P_3 intersec M p1p3 p2p4 line om O M perp l M om intersec X l p2p3 intersec Y l p1p4 cmark_l P_1 cmark_l P_2 cmark_lt P_3 cmark_b P_4 cmark_b O cmark_lt M cmark_l X cmark_t Y drawcircle k drawdashline p1p3 drawdashline p2p4 drawdashline p1p4 drawdashline p2p3 drawsegment X Y ','2008/01/09','', 'gpreda1 ')
gclc figure0049.code figure0049.pic > figure0049.errors
Warning: fread() [function.fread]: Length parameter must be greater than 0 in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 328
Figura 384

    * Figure
    * figure0049.jpg
    * Description of the construction in natural language
    * figure0049.xml
    * Figure in SVG format
    * figure0049.svg

INSERT INTO demonstrations (teoId,proverId,code,dateSubmission,bibref,userId) VALUES ('GEO0049','2',' point P_1 32 40 point O 62 40 circle k O P_1 oncircle P_2 O P_1 oncircle P_3 O P_1 oncircle P_4 O P_1 line p1p3 P_1 P_3 line p2p4 P_2 P_4 line p1p4 P_1 P_4 line p2p3 P_2 P_3 intersec M p1p3 p2p4 line om O M perp l M om intersec X l p2p3 intersec Y l p1p4 prove { equal { sratio X M M Y } { 1 } } ','2008/01/09', '','gpreda1 ')
The Proof's code 0049 is correct.

Processing the XML file, please wait
/usr/local/bin/gclc proof0049.code proofCode0049.xml -xml > proof0049.errors
Warning: fread() [function.fread]: Length parameter must be greater than 0 in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 497

INSERT INTO theorems (teoId,userId,category,description,shortDescription,teoName,dateSubmission) VALUES ('GEO0050','gpreda1 ','Geometry','\\begin{geothm} Prove that the angle over circle diameter is right angle. \\end{geothm}',' ', ' Right Angle over Circle Diameter ','2008/01/09')

INSERT INTO bibtheorem (teoId,bibrefId) VALUES ('GEO0047','chou88')

INSERT INTO figures (teoId,drawerId,code,dateSubmission,bibref,userId) VALUES ('GEO0050','3',' dim 110 110 point A 20 55 point B 90 55 midpoint O A B circle k O A point C 76.49 82.62 cmark_t C drawsegment A C drawsegment B C drawcircle k cmark_l A cmark_r B drawsegment A B ','2008/01/09','', 'gpreda1 ')
gclc figure0050.code figure0050.pic > figure0050.errors
Warning: fread() [function.fread]: Length parameter must be greater than 0 in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 328
Figura 392

    * Figure
    * figure0050.jpg
    * Description of the construction in natural language
    * figure0050.xml
    * Figure in SVG format
    * figure0050.svg

INSERT INTO demonstrations (teoId,proverId,code,dateSubmission,bibref,userId) VALUES ('GEO0050','2',' point A 20 55 point B 90 55 midpoint O A B circle k O A oncircle C O A prove { equal { ratio 1 { angle A C B } } { 0 } } ','2008/01/09', '','gpreda1 ')
The Proof's code 0050 is correct.

Processing the XML file, please wait
/usr/local/bin/gclc proof0050.code proofCode0050.xml -xml > proof0050.errors
Warning: fopen(proof0050.xml.bz2) [function.fopen]: failed to open stream: No such file or directory in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 508

Warning: filesize() [function.filesize]: stat failed for proof0050.xml.bz2 in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 509

Warning: fread(): supplied argument is not a valid stream resource in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 509

Warning: fclose(): supplied argument is not a valid stream resource in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 511

INSERT INTO theorems (teoId,userId,category,description,shortDescription,teoName,dateSubmission) VALUES ('GEO0051','gpreda1 ','Geometry','\\begin{geothm} Let a quadrilateral $ABCD$ be inscribed in a circle. Then the sum of the products of the two pairs of opposite sides equals the product of its two diagonals. In other words, $AD \\cdot BC + AB \\cdot CD = AC \\cdot BD$. \\end{geothm}',' ', ' Ptolemy s Theorem ','2008/01/09')

INSERT INTO bibtheorem (teoId,bibrefId) VALUES ('GEO0047','chou88')

INSERT INTO figures (teoId,drawerId,code,dateSubmission,bibref,userId) VALUES ('GEO0051','3',' dim 110 95 point A 20 30 point B 90 30 point C 60 80 med p A B med q B C intersec O p q circle k O A point D 30.42 71.10 cmark_lb A cmark_rb B cmark_rt C cmark_lt D cmark_b O drawsegment A B drawsegment A D drawsegment A D drawsegment C B drawsegment D B drawsegment C D drawsegment C A drawcircle k ','2008/01/09','', 'gpreda1 ')
gclc figure0051.code figure0051.pic > figure0051.errors
Warning: fread() [function.fread]: Length parameter must be greater than 0 in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 328
Figura 400

    * Figure
    * figure0051.jpg
    * Description of the construction in natural language
    * figure0051.xml
    * Figure in SVG format
    * figure0051.svg

INSERT INTO demonstrations (teoId,proverId,code,dateSubmission,bibref,userId) VALUES ('GEO0051','2',' point A 20 30 point B 90 30 point C 60 80 med p A B med q B C intersec O p q circle k O A oncircle D O A prove { alg_sum_zero3 { mult { segment A B } { segment C D } } { mult { segment A D } { segment B C } } { mult { segment A C } { segment B D } } } ','2008/01/09', '','gpreda1 ')
The Proof's code 0051 is correct.

Processing the XML file, please wait
/usr/local/bin/gclc proof0051.code proofCode0051.xml -xml > proof0051.errors
Warning: fopen(proof0051.xml.bz2) [function.fopen]: failed to open stream: No such file or directory in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 508

Warning: filesize() [function.filesize]: stat failed for proof0051.xml.bz2 in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 509

Warning: fread(): supplied argument is not a valid stream resource in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 509

Warning: fclose(): supplied argument is not a valid stream resource in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 511

INSERT INTO theorems (teoId,userId,category,description,shortDescription,teoName,dateSubmission) VALUES ('GEO0052','gpreda1 ','Geometry','\\begin{geothm} There is a point $P$ inside of triangle $ABC$. Lines $PA$, $PB$ and $PC$ meet the triangle at three points $D$, $E$ and $F$. Show that: $\\frac{\\overline{AF}}{\\overline{FB}} \\cdot \\frac{\\overline{BD}}{\\overline{DC}} \\cdot \\frac{\\overline{CE}}{\\overline{EA}} = 1$. \\end{geothm}',' ', ' Ceva s theorem ','2008/01/09')

INSERT INTO bibtheorem (teoId,bibrefId) VALUES ('GEO0047','chou88')

INSERT INTO figures (teoId,drawerId,code,dateSubmission,bibref,userId) VALUES ('GEO0052','3',' dim 100 100 point A 60 10 point B 30 90 point C 80 90 point P 55 75 line bc B C line pa P A line ac A C line pb P B line ab A B line pc P C intersec D bc pa intersec E ac pb intersec F ab pc drawsegment A B drawsegment A C drawsegment B C drawsegment A D drawsegment B E drawsegment C F cmark_b A cmark_t B cmark_t C cmark_t D cmark_l F cmark_r E cmark_rt P ','2008/01/09','', 'gpreda1 ')
gclc figure0052.code figure0052.pic > figure0052.errors
Warning: fread() [function.fread]: Length parameter must be greater than 0 in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 328
Figura 408

    * Figure
    * figure0052.jpg
    * Description of the construction in natural language
    * figure0052.xml
    * Figure in SVG format
    * figure0052.svg

INSERT INTO demonstrations (teoId,proverId,code,dateSubmission,bibref,userId) VALUES ('GEO0052','2',' point A 60 10 point B 30 90 point C 80 90 point P 55 75 line bc B C line pa P A line ac A C line pb P B line ab A B line pc P C intersec D bc pa intersec E ac pb intersec F ab pc prove { equal { mult { mult { sratio A F F B } { sratio B D D C } } { sratio C E E A } } 1 } ','2008/01/09', '','gpreda1 ')
The Proof's code 0052 is correct.

Processing the XML file, please wait
/usr/local/bin/gclc proof0052.code proofCode0052.xml -xml > proof0052.errors
Warning: fread() [function.fread]: Length parameter must be greater than 0 in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 497

INSERT INTO theorems (teoId,userId,category,description,shortDescription,teoName,dateSubmission) VALUES ('GEO0053','gpreda1 ','Geometry','\\begin{geothm} Given triangle $ABC$, let $p$ be line through $A$ parallel with $BC$, and let $q$ be line through $C$ parallel with $AB$. Let $p$ and $q$ intersects at $D$. Let $BD$ intersect $AC$ at $E$. Show that: $\\overline{AE} = \\overline{EC}$. \\end{geothm}',' ', ' Parallelogram Theorem 2 ','2008/01/09')

INSERT INTO bibtheorem (teoId,bibrefId) VALUES ('GEO0047','chou88')

INSERT INTO figures (teoId,drawerId,code,dateSubmission,bibref,userId) VALUES ('GEO0053','3',' dim 130 70 point A 20 20 point B 80 20 point C 97.60 51.50 line ab A B line bc B C parallel p A bc parallel q C ab intersec D p q cmark_b A cmark_b B cmark_t C cmark_t D drawsegment A B drawsegment C B drawsegment A D drawsegment C D line ac A C line bd B D intersec E ac bd cmark_t E drawdashsegment A C drawdashsegment B D ','2008/01/09','', 'gpreda1 ')
gclc figure0053.code figure0053.pic > figure0053.errors
Warning: fread() [function.fread]: Length parameter must be greater than 0 in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 328
Figura 416

    * Figure
    * figure0053.jpg
    * Description of the construction in natural language
    * figure0053.xml
    * Figure in SVG format
    * figure0053.svg

INSERT INTO demonstrations (teoId,proverId,code,dateSubmission,bibref,userId) VALUES ('GEO0053','2',' point A 20 20 point B 80 20 point C 97.60 51.50 line ab A B line bc B C parallel p A bc parallel q C ab intersec D p q line ac A C line bd B D intersec E ac bd prove { equal { sratio A E E C } { 1 } } prove { same_length A E E C } ','2008/01/09', '','gpreda1 ')
The Proof's code 0053 is correct.

Processing the XML file, please wait
/usr/local/bin/gclc proof0053.code proofCode0053.xml -xml > proof0053.errors
Warning: fread() [function.fread]: Length parameter must be greater than 0 in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 497

INSERT INTO theorems (teoId,userId,category,description,shortDescription,teoName,dateSubmission) VALUES ('GEO0054','gpreda1 ','Geometry','\\begin{geothm} Show that each triangle has circumscribed circle. \\end{geothm}',' ', ' Circumscribed Circle Exists Theorem ','2008/01/09')

INSERT INTO bibtheorem (teoId,bibrefId) VALUES ('GEO0047','chou88')

INSERT INTO figures (teoId,drawerId,code,dateSubmission,bibref,userId) VALUES ('GEO0054','3',' dim 95 95 point A 30 20 point B 70 20 point C 60 80 med b A C med a C B intersec O a b midpoint M A B drawsegment A B drawsegment A C drawsegment B C drawsegment A O drawsegment B O drawsegment C O cmark_b A cmark_b B cmark_t C cmark_l O drawcircle O A drawdashsegment O M cmark_b M ','2008/01/09','', 'gpreda1 ')
gclc figure0054.code figure0054.pic > figure0054.errors
Warning: fread() [function.fread]: Length parameter must be greater than 0 in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 328
Figura 424

    * Figure
    * figure0054.jpg
    * Description of the construction in natural language
    * figure0054.xml
    * Figure in SVG format
    * figure0054.svg

INSERT INTO demonstrations (teoId,proverId,code,dateSubmission,bibref,userId) VALUES ('GEO0054','2',' point A 30 20 point B 70 20 point C 60 80 med b A C med a C B intersec O a b midpoint M A B prove { perpendicular O M A B } ','2008/01/09', '','gpreda1 ')
The Proof's code 0054 is correct.

Processing the XML file, please wait
/usr/local/bin/gclc proof0054.code proofCode0054.xml -xml > proof0054.errors
Warning: fread() [function.fread]: Length parameter must be greater than 0 in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 497

INSERT INTO theorems (teoId,userId,category,description,shortDescription,teoName,dateSubmission) VALUES ('GEO0055','gpreda1 ','Geometry','\\begin{geothm} If we draw line segments between the midpoints, in order, of any quadrilateral, we get a parallelogram which has half the area of the original quadrilateral. \\end{geothm}',' ', ' Varignon s Theorem ','2008/01/09')

INSERT INTO bibtheorem (teoId,bibrefId) VALUES ('GEO0047','chou88')

INSERT INTO figures (teoId,drawerId,code,dateSubmission,bibref,userId) VALUES ('GEO0055','3',' dim 100 100 point A 20 20 point B 80 20 point C 70 70 point D 30 50 midpoint P A B midpoint Q B C midpoint R C D midpoint S D A cmark_b A cmark_b B cmark_t C cmark_t D cmark_b P cmark_r Q cmark_t R cmark_l S drawsegment A B drawsegment C B drawsegment C D drawsegment A D drawdashsegment P Q drawdashsegment R Q drawdashsegment R S drawdashsegment P S ','2008/01/09','', 'gpreda1 ')
gclc figure0055.code figure0055.pic > figure0055.errors
Warning: fread() [function.fread]: Length parameter must be greater than 0 in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 328
Figura 432

    * Figure
    * figure0055.jpg
    * Description of the construction in natural language
    * figure0055.xml
    * Figure in SVG format
    * figure0055.svg

INSERT INTO demonstrations (teoId,proverId,code,dateSubmission,bibref,userId) VALUES ('GEO0055','2',' point A 20 20 point B 80 20 point C 70 70 point D 30 50 midpoint P A B midpoint Q B C midpoint R C D midpoint S D A prove { parallel P Q R S } prove { same_length P Q R S } ','2008/01/09', '','gpreda1 ')
The Proof's code 0055 is correct.

Processing the XML file, please wait
/usr/local/bin/gclc proof0055.code proofCode0055.xml -xml > proof0055.errors
Warning: fread() [function.fread]: Length parameter must be greater than 0 in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 497

INSERT INTO theorems (teoId,userId,category,description,shortDescription,teoName,dateSubmission) VALUES ('GEO0056','gpreda1 ','Geometry','\\begin{geothm} Quadrilateral $ABCD$ is given such that diagonals $AC$ and $BD$ intersect at right angle. Let $A_1$, $B_1$, $C_1$ and $D_1$ be midpoints of quadrilateral sides $AB$, $BC$, $CD$ and $DA$ respectively. Let $A_2$, $B_2$, $C_2$ and $D_2$ be feet from points $A_1$, $B_1$, $C_1$ and $D_1$ upon lines $CD$, $DA$, $AB$ and $BC$ respectively. Show that eight points $A_1$, $B_1$, $C_1$, $D_1$, $A_2$, $B_2$, $C_2$ and $D_2$ lie on a circle. \\end{geothm}',' ', ' Eight Points Circle ','2008/01/09')

INSERT INTO bibtheorem (teoId,bibrefId) VALUES ('GEO0047','chou88')

INSERT INTO figures (teoId,drawerId,code,dateSubmission,bibref,userId) VALUES ('GEO0056','3',' dim 130 110 point A 20 35 point C 110 35 point B 80 20 point D 80 75 midpoint A_1 A B midpoint B_1 B C midpoint C_1 C D midpoint D_1 D A line cd C D line da D A line ab A B line bc B C foot A_2 A_1 cd foot B_2 B_1 da foot C_2 C_1 ab foot D_2 D_1 bc midpoint O A_1 C_1 circle k O A_1 drawcircle k drawsegment A B drawsegment C B drawsegment A D drawsegment A C drawsegment D B drawsegment D C drawdashsegment A_1 A_2 drawdashsegment B_1 B_2 drawdashsegment C_1 C_2 drawdashsegment D_1 D_2 drawdashsegment B D_2 drawdashsegment B C_2 cmark_b A cmark_b B cmark_b C cmark_t D cmark_b A_1 cmark_rb B_1 cmark_rt C_1 cmark_lt D_1 cmark_rt A_2 cmark_lt B_2 cmark_b C_2 cmark_b D_2 ','2008/01/09','', 'gpreda1 ')
gclc figure0056.code figure0056.pic > figure0056.errors
Warning: fread() [function.fread]: Length parameter must be greater than 0 in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 328
Figura 440

    * Figure
    * figure0056.jpg
    * Description of the construction in natural language
    * figure0056.xml
    * Figure in SVG format
    * figure0056.svg

INSERT INTO demonstrations (teoId,proverId,code,dateSubmission,bibref,userId) VALUES ('GEO0056','2',' point A 20 35 point C 110 35 point B 80 20 point D 80 75 midpoint A_1 A B midpoint B_1 B C midpoint C_1 C D midpoint D_1 D A line cd C D line da D A line ab A B line bc B C foot A_2 A_1 cd foot B_2 B_1 da foot C_2 C_1 ab foot D_2 D_1 bc midpoint O A_1 C_1 circle k O A_1 prove { perpendicular A_1 B_1 B_1 C_1 } prove { perpendicular A_1 D_1 D_1 C_1 } prove { perpendicular A_1 A_2 A_2 C_1 } ','2008/01/09', '','gpreda1 ')
The Proof's code 0056 is correct.

Processing the XML file, please wait
/usr/local/bin/gclc proof0056.code proofCode0056.xml -xml > proof0056.errors
Warning: fread() [function.fread]: Length parameter must be greater than 0 in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 497

INSERT INTO theorems (teoId,userId,category,description,shortDescription,teoName,dateSubmission) VALUES ('GEO0057','gpreda1 ','Geometry','\\begin{geothm} A line passing through the intersection $O$ of the diagonals of parallelogram $ABCD$ meets the four sides at $E$, $F$, $G$, $H$. Show that $EF \\cong GH$. \\end{geothm}',' ', ' Example 84 ','2008/01/09')

INSERT INTO bibtheorem (teoId,bibrefId) VALUES ('GEO0057','chou88')

INSERT INTO figures (teoId,drawerId,code,dateSubmission,bibref,userId) VALUES ('GEO0057','3',' dim 130 110 point A 30 30 point B 110 30 point C 90 80 line ab A B line bc B C parallel cd C ab parallel ad A bc intersec D cd ad point H 79.97 105.07 line bd B D line ac A C intersec O ac bd line oh O H intersec F oh cd intersec G oh ab intersec E oh ad cmark_lb A cmark_b B cmark_r C cmark_t D cmark_lt F cmark_b O cmark_l H cmark_r E drawsegment A B drawsegment H B drawsegment C D drawsegment E D drawsegment E H drawsegment A C drawsegment B D ','2008/01/09','chou88', 'gpreda1 ')
gclc figure0057.code figure0057.pic > figure0057.errors
Warning: fread() [function.fread]: Length parameter must be greater than 0 in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 328
Figura 448

    * Figure
    * figure0057.jpg
    * Description of the construction in natural language
    * figure0057.xml
    * Figure in SVG format
    * figure0057.svg

INSERT INTO demonstrations (teoId,proverId,code,dateSubmission,bibref,userId) VALUES ('GEO0057','2',' point A 30 30 point B 110 30 point C 90 80 line ab A B line bc B C parallel cd C ab parallel ad A bc intersec D cd ad online H B C line bd B D line ac A C intersec O ac bd line oh O H intersec F oh cd intersec G oh ab intersec E oh ad prove { equal { sratio E F G H } { 1 } } ','2008/01/09', '','gpreda1 ')
The Proof's code 0057 is correct.

Processing the XML file, please wait
/usr/local/bin/gclc proof0057.code proofCode0057.xml -xml > proof0057.errors
Warning: fread() [function.fread]: Length parameter must be greater than 0 in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 497

INSERT INTO theorems (teoId,userId,category,description,shortDescription,teoName,dateSubmission) VALUES ('GEO0058','gpreda1 ','Geometry','\\begin{geothm} Let $D$ be a point on the side $CB$ of a right triangle $ABC$ such that the circle ($O$) with diameter $CD$ touches the hypotenuses $AB$ at $E$. Let $F = AC \\cap DE$. Show that $AF \\cong AE$ \\end{geothm}',' ', ' Example 91 ','2008/01/09')

INSERT INTO bibtheorem (teoId,bibrefId) VALUES ('GEO0058','chou88')

INSERT INTO figures (teoId,drawerId,code,dateSubmission,bibref,userId) VALUES ('GEO0058','3',' dim 130 110 point C 20 30 point D 70 30 line cd C D midpoint O C D circle k O C point E 53.34 53.57 line oe O E perp ab E oe perp ac C cd intersec A ac ab intersec B ab cd line de D E intersec F de ac cmark_lb C cmark_b O cmark_rb D cmark_rt E cmark_l A cmark_b B cmark_l F drawcircle k drawsegment C B drawsegment A B drawsegment C F drawsegment O E drawsegment D F ','2008/01/09','chou88', 'gpreda1 ')
gclc figure0058.code figure0058.pic > figure0058.errors
Warning: fread() [function.fread]: Length parameter must be greater than 0 in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 328
Figura 456

    * Figure
    * figure0058.jpg
    * Description of the construction in natural language
    * figure0058.xml
    * Figure in SVG format
    * figure0058.svg

INSERT INTO demonstrations (teoId,proverId,code,dateSubmission,bibref,userId) VALUES ('GEO0058','2',' point C 20 30 point D 70 30 line cd C D midpoint O C D circle k O C oncircle E O C line oe O E perp ab E oe perp ac C cd intersec A ac ab intersec B ab cd line de D E intersec F de ac prove { equal { segment A F } { segment A E } } ','2008/01/09', '','gpreda1 ')
The Proof's code 0058 is correct.

Processing the XML file, please wait
/usr/local/bin/gclc proof0058.code proofCode0058.xml -xml > proof0058.errors
Warning: fopen(proof0058.xml.bz2) [function.fopen]: failed to open stream: No such file or directory in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 508

Warning: filesize() [function.filesize]: stat failed for proof0058.xml.bz2 in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 509

Warning: fread(): supplied argument is not a valid stream resource in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 509

Warning: fclose(): supplied argument is not a valid stream resource in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 511

INSERT INTO theorems (teoId,userId,category,description,shortDescription,teoName,dateSubmission) VALUES ('GEO0059','gpreda1 ','Geometry','\\begin{geothm} Three equal squares are placed side by side, as it is shown on the picture. Show that: $\\angle D_1AD + \\angle D_1BD = \\angle D_1CD$. \\end{geothm}',' ', ' Three squares ','2008/01/09')

INSERT INTO bibtheorem (teoId,bibrefId) VALUES ('GEO0058','chou88')

INSERT INTO figures (teoId,drawerId,code,dateSubmission,bibref,userId) VALUES ('GEO0059','3',' dim 130 90 point A 20 20 point B 50 20 towards C A B 2 towards D A B 3 line ab A B perp a A ab circle k A B intersec2 A_1 A_2 k a perp ab1 A_1 a perp b B ab perp c C ab perp d D ab intersec B_1 ab1 b intersec C_1 ab1 c intersec D_1 ab1 d cmark_t A_1 cmark_b A cmark_b B cmark_b C cmark_b D cmark_t D_1 drawsegment A D drawsegment A_1 D_1 drawsegment A A_1 drawsegment B B_1 drawsegment C C_1 drawsegment D D_1 drawdashsegment D_1 A drawdashsegment D_1 B drawdashsegment D_1 C ','2008/01/09','', 'gpreda1 ')
gclc figure0059.code figure0059.pic > figure0059.errors
Warning: fread() [function.fread]: Length parameter must be greater than 0 in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 328
Figura 464

    * Figure
    * figure0059.jpg
    * Description of the construction in natural language
    * figure0059.xml
    * Figure in SVG format
    * figure0059.svg

INSERT INTO demonstrations (teoId,proverId,code,dateSubmission,bibref,userId) VALUES ('GEO0059','2',' point A 20 20 point B 50 20 towards C A B 2 towards D A B 3 line ab A B perp a A ab circle k A B intersec2 A_1 A_2 k a perp ab1 A_1 a perp d D ab intersec D_1 ab1 d prove { equal { angle D_1 C D } { sum { mult { angle D_1 A D } { mult { angle D_1 B D } { angle D_1 C D } } } { sum { angle D_1 A D } { angle D_1 B D } } } } ','2008/01/09', '','gpreda1 ')
The Proof's code 0059 is correct.

Processing the XML file, please wait
/usr/local/bin/gclc proof0059.code proofCode0059.xml -xml > proof0059.errors
Warning: fopen(proof0059.xml.bz2) [function.fopen]: failed to open stream: No such file or directory in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 508

Warning: filesize() [function.filesize]: stat failed for proof0059.xml.bz2 in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 509

Warning: fread(): supplied argument is not a valid stream resource in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 509

Warning: fclose(): supplied argument is not a valid stream resource in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 511

INSERT INTO theorems (teoId,userId,category,description,shortDescription,teoName,dateSubmission) VALUES ('GEO0060','gpreda1 ','Geometry','\\begin{geothm} From the ends $D$ and $C$ of a diameter of circle $(O)$ perpendiculars are drawn to chort $AB$. Let $E$ and $F$ be the feet of the perpendiculars. Show that $OE \\cong OF$. \\end{geothm}',' ', ' Example 92 ','2008/01/09')

INSERT INTO bibtheorem (teoId,bibrefId) VALUES ('GEO0060','chou88')

INSERT INTO figures (teoId,drawerId,code,dateSubmission,bibref,userId) VALUES ('GEO0060','3',' dim 130 110 point A 25 30 point B 105 30 point X 100 100 point Y 92 90 line xy X Y med m A B intersec O m xy circle k O A point Z 80 80 line cd O Z intersec2 D C k cd line ab A B foot E C ab foot F D ab cmark_lb A cmark_rb B cmark_lt O cmark_lb C cmark_rt D cmark_t E cmark_b F drawcircle k drawdashsegment O E drawdashsegment O F drawsegment A B drawsegment C D drawsegment C E drawsegment D F ','2008/01/09','chou88', 'gpreda1 ')
gclc figure0060.code figure0060.pic > figure0060.errors
Warning: fread() [function.fread]: Length parameter must be greater than 0 in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 328
Figura 472

    * Figure
    * figure0060.jpg
    * Description of the construction in natural language
    * figure0060.xml
    * Figure in SVG format
    * figure0060.svg

INSERT INTO demonstrations (teoId,proverId,code,dateSubmission,bibref,userId) VALUES ('GEO0060','2',' point A 25 30 point B 105 30 point X 100 100 point Y 92 90 line xy X Y med m A B intersec O m xy circle k O A point Z 80 80 line cd O Z intersec2 D C k cd line ab A B foot E C ab foot F D ab prove { equal { segment O E } { segment O F } } ','2008/01/09', '','gpreda1 ')
The Proof's code 0060 is correct.

Processing the XML file, please wait
/usr/local/bin/gclc proof0060.code proofCode0060.xml -xml > proof0060.errors
Warning: fopen(proof0060.xml.bz2) [function.fopen]: failed to open stream: No such file or directory in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 508

Warning: filesize() [function.filesize]: stat failed for proof0060.xml.bz2 in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 509

Warning: fread(): supplied argument is not a valid stream resource in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 509

Warning: fclose(): supplied argument is not a valid stream resource in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 511

INSERT INTO theorems (teoId,userId,category,description,shortDescription,teoName,dateSubmission) VALUES ('GEO0061','gpreda1 ','Geometry','\\begin{geothm} Through $P$ a tangent $PE$ and a secant $PAB$ of circle $(O)$ are drawn. The bisector of angle $APE$ meets $AE$ and $BE$ at $C$ and $D$. Show that $EC \\cong ED$. \\end{geothm}',' ', ' Example 94 ','2008/01/09')

INSERT INTO bibtheorem (teoId,bibrefId) VALUES ('GEO0061','chou88')

INSERT INTO figures (teoId,drawerId,code,dateSubmission,bibref,userId) VALUES ('GEO0061','3',' dim 110 90 point E 35 20 point O 35 45 circle k O E point A 17.71 63.06 point B 58.58 36.68 line ab A B line oe O E perp ep E oe intersec P ep ab line ae A E line be B E bis p E P A intersec C ae p intersec D be p cmark_t O cmark_b E cmark_b P cmark_lt A cmark_r B cmark_lb C cmark_t D drawsegment E P drawsegment E O drawsegment A P drawsegment A E drawsegment A B drawcircle k drawdashline p drawsegment E A drawsegment E B ','2008/01/09','chou88', 'gpreda1 ')
gclc figure0061.code figure0061.pic > figure0061.errors
Warning: fread() [function.fread]: Length parameter must be greater than 0 in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 328
Figura 480

    * Figure
    * figure0061.jpg
    * Description of the construction in natural language
    * figure0061.xml
    * Figure in SVG format
    * figure0061.svg

INSERT INTO demonstrations (teoId,proverId,code,dateSubmission,bibref,userId) VALUES ('GEO0061','2',' point E 35 20 point O 35 45 circle k O E oncircle A O E oncircle B O E line ab A B line oe O E perp ep E oe intersec P ep ab line ae A E line be B E bis p E P A intersec C ae p intersec D be p prove { equal { segment E D } { segment E C } } ','2008/01/09', '','gpreda1 ')
The Proof's code 0061 is correct.

Processing the XML file, please wait
/usr/local/bin/gclc proof0061.code proofCode0061.xml -xml > proof0061.errors
Warning: fopen(proof0061.xml.bz2) [function.fopen]: failed to open stream: No such file or directory in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 508

Warning: filesize() [function.filesize]: stat failed for proof0061.xml.bz2 in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 509

Warning: fread(): supplied argument is not a valid stream resource in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 509

Warning: fclose(): supplied argument is not a valid stream resource in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 511

INSERT INTO theorems (teoId,userId,category,description,shortDescription,teoName,dateSubmission) VALUES ('GEO0062','gpreda1 ','Geometry','\\begin{geothm} Assume the incircle of $\\triangle ABC$ touches the sides $BC$, $AC$ and $AB$ in points $D$, $E$ and $F$ respectively. Show that lines $AD$, $BE$ and $CF$ meet at the Gergonne point $G$ of the triangle. \\end{geothm}',' ', ' Gergonne point ','2008/01/09')

INSERT INTO bibtheorem (teoId,bibrefId) VALUES ('GEO0061','chou88')

INSERT INTO figures (teoId,drawerId,code,dateSubmission,bibref,userId) VALUES ('GEO0062','3',' dim 100 100 point A 20 20 point B 80 20 point C 70 70 bis ba B A C bis bb C B A bis bc A C B line a B C line b A C line c A B intersec I ba bb foot D I a foot E I b foot F I c circle k I F line ad A D line be B E line cf C F intersec G ad be cmark_b A cmark_b B cmark_t C cmark_b F cmark_lt E cmark_rt D cmark_lt G drawcircle k drawsegment A B drawsegment C B drawsegment C A drawdashsegment A D drawdashsegment B E drawdashsegment C F ','2008/01/09','', 'gpreda1 ')
gclc figure0062.code figure0062.pic > figure0062.errors
Warning: fread() [function.fread]: Length parameter must be greater than 0 in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 328
Figura 488

    * Figure
    * figure0062.jpg
    * Description of the construction in natural language
    * figure0062.xml
    * Figure in SVG format
    * figure0062.svg

INSERT INTO demonstrations (teoId,proverId,code,dateSubmission,bibref,userId) VALUES ('GEO0062','2',' point A 20 20 point B 80 20 point C 70 70 bis ba B A C bis bb C B A bis bc A C B line a B C line b A C line c A B intersec I ba bb foot D I a foot E I b foot F I c line ad A D line be B E line cf C F intersec G ad be prove { collinear C F G } ','2008/01/09', '','gpreda1 ')
The Proof's code 0062 is correct.

Processing the XML file, please wait
/usr/local/bin/gclc proof0062.code proofCode0062.xml -xml > proof0062.errors
Warning: fread() [function.fread]: Length parameter must be greater than 0 in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 497

INSERT INTO theorems (teoId,userId,category,description,shortDescription,teoName,dateSubmission) VALUES ('GEO0063','gpreda1 ','Geometry','\\begin{geothm} Assume the incircle of $\\triangle ABC$ touches the sides $BC$, $AC$ and $AB$ in points $D$, $E$ and $F$ respectively. The lines $AD$, $BE$ and $CF$ meet at the Gergonne point $G$ of the triangle. $DEF$ is known as Gergonne triangle (and also contact triangle) of $\\triangle ABC$. Suppose three lines are drawn through $G$ parallel to the sides of the Gergonne triangle. These meet the sides of $\\triangle ABC$ in six points $P$, $Q$, $R$, $S$, $T$ and $U$. Show that six points are concyclic. Moreover, the circle they lie on is centered at the incenter. \\end{geothm}',' ', ' Adams Circle ','2008/01/09')

INSERT INTO bibtheorem (teoId,bibrefId) VALUES ('GEO0061','chou88')

INSERT INTO figures (teoId,drawerId,code,dateSubmission,bibref,userId) VALUES ('GEO0063','3',' dim 130 130 point A 20 20 point B 110 20 point C 95 105 bis ba B A C bis bb C B A bis bc A C B line a B C line b A C line c A B intersec I ba bb foot D I a foot E I b foot F I c circle k I F line ad A D line be B E line cf C F intersec G ad be line de D E line df D F line ef E F parallel gpq G de parallel grs G df parallel gtu G ef intersec P gpq b intersec Q gpq a intersec R grs a intersec S grs c intersec T gtu c intersec U gtu b cmark_l I cmark_b A cmark_b B cmark_t C cmark_b F cmark_lt E cmark_rt D cmark_rb G cmark_lt P cmark_r Q cmark_rt R cmark_b S cmark_b T cmark_lt U drawcircle k drawsegment A B drawsegment C B drawsegment C A drawsegment A D drawsegment B E drawsegment C F drawdashsegment P Q drawdashsegment R S drawdashsegment T U drawsegment D E drawsegment D F drawsegment F E circle k1 I S drawdashcircle k1 ','2008/01/09','', 'gpreda1 ')
gclc figure0063.code figure0063.pic > figure0063.errors
Figura 496

    * Figure
    * figure0063.jpg
    * Description of the construction in natural language
    * figure0063.xml
    * Figure in SVG format
    * figure0063.svg

INSERT INTO demonstrations (teoId,proverId,code,dateSubmission,bibref,userId) VALUES ('GEO0063','2',' point A 20 20 point B 110 20 point C 95 105 bis ba B A C bis bb C B A bis bc A C B line a B C line b A C line c A B intersec I ba bb foot D I a foot E I b foot F I c line ad A D line be B E line cf C F intersec G ad be line de D E line df D F line ef E F parallel gpq G de parallel grs G df parallel gtu G ef intersec Q gpq a intersec S grs c intersec T gtu c prove { equal { segment I S } { segment I T } } prove { equal { segment I S } { segment I Q } } ','2008/01/09', '','gpreda1 ')
The Proof's code 0063 is correct.

Processing the XML file, please wait
/usr/local/bin/gclc proof0063.code proofCode0063.xml -xml > proof0063.errors
Warning: fopen(proof0063.xml.bz2) [function.fopen]: failed to open stream: No such file or directory in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 508

Warning: filesize() [function.filesize]: stat failed for proof0063.xml.bz2 in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 509

Warning: fread(): supplied argument is not a valid stream resource in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 509

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INSERT INTO theorems (teoId,userId,category,description,shortDescription,teoName,dateSubmission) VALUES ('GEO0064','gpreda1 ','Geometry','\\begin{geothm} Let $ABCD$ be a square. $CG$ is parallel to the diagonal $BD$. Point $E$ is on $CG$ such that $BE \\cong BD$. $F$ is the intersection of $BE$ and $DC$. Show that $DF \\cong DE$. \\end{geothm}',' ', ' Example 5.1 ','2008/01/09')

INSERT INTO bibtheorem (teoId,bibrefId) VALUES ('GEO0064','chou88')

INSERT INTO figures (teoId,drawerId,code,dateSubmission,bibref,userId) VALUES ('GEO0064','3',' dim 110 60 point A 59 20 point B 78 20 line ab A B perp p A ab circle k A B intersec2 D D_1 k p perp q D p perp r B ab intersec C q r line d B D parallel c C d circle k1 B D intersec2 E E_1 k1 c line be B E line cd C D intersec F be cd line be1 B E_1 intersec F_1 be1 cd cmark_b A cmark_b B cmark_t D cmark_t C cmark_t E cmark_lb F cmark_rt E_1 cmark_t F_1 drawsegment A B drawsegment A D drawsegment C B drawsegment F_1 C drawsegment B D drawsegment B E drawsegment E D drawsegment C E drawsegment E E_1 drawsegment F_1 E_1 drawdashsegment D E_1 ','2008/01/09','chou88', 'gpreda1 ')
gclc figure0064.code figure0064.pic > figure0064.errors
Warning: fread() [function.fread]: Length parameter must be greater than 0 in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 328
Figura 504

    * Figure
    * figure0064.jpg
    * Description of the construction in natural language
    * figure0064.xml
    * Figure in SVG format
    * figure0064.svg

INSERT INTO demonstrations (teoId,proverId,code,dateSubmission,bibref,userId) VALUES ('GEO0064','2',' point A 59 20 point B 78 20 line ab A B perp p A ab circle k A B intersec2 D D_1 k p perp q D p perp r B ab intersec C q r line d B D parallel c C d circle k1 B D intersec2 E E_1 k1 c line be B E line cd C D intersec F be cd prove { equal { segment D F } { segment D E } } ','2008/01/09', '','gpreda1 ')
The Proof's code 0064 is correct.

Processing the XML file, please wait
/usr/local/bin/gclc proof0064.code proofCode0064.xml -xml > proof0064.errors
Warning: fopen(proof0064.xml.bz2) [function.fopen]: failed to open stream: No such file or directory in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 508

Warning: filesize() [function.filesize]: stat failed for proof0064.xml.bz2 in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 509

Warning: fread(): supplied argument is not a valid stream resource in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 509

Warning: fclose(): supplied argument is not a valid stream resource in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 511

INSERT INTO theorems (teoId,userId,category,description,shortDescription,teoName,dateSubmission) VALUES ('GEO0065','gpreda1 ','Geometry','\\begin{geothm} Let $M$ be the midpoint of the arc $AB$ of circle $(O)$, $D$ be the midpoint of $AB$. he perpendicular through $M$ is drawn to the tangent of the circle at $A$ meeting that tangent at $E$. Show $ME \\cong MD$. \\end{geothm}',' ', ' Example 95 ','2008/01/09')

INSERT INTO bibtheorem (teoId,bibrefId) VALUES ('GEO0065','chou88')

INSERT INTO figures (teoId,drawerId,code,dateSubmission,bibref,userId) VALUES ('GEO0065','3',' dim 100 100 point D 50 33 point O 50 55 line d O D point M 50 90 circle k O M perp a D d intersec2 B A k a line p A O perp q A p parallel r M p intersec E r q cmark_t E cmark_lb A cmark_rb B cmark_r O cmark_b D cmark_t M drawcircle k drawsegment A B drawsegment A O drawsegment M D drawsegment E M drawsegment A E ','2008/01/09','chou88', 'gpreda1 ')
gclc figure0065.code figure0065.pic > figure0065.errors
Warning: fread() [function.fread]: Length parameter must be greater than 0 in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 328
Figura 512

    * Figure
    * figure0065.jpg
    * Description of the construction in natural language
    * figure0065.xml
    * Figure in SVG format
    * figure0065.svg

INSERT INTO demonstrations (teoId,proverId,code,dateSubmission,bibref,userId) VALUES ('GEO0065','2',' point D 50 33 point O 50 55 line d O D point M 50 90 circle k O M perp a D d intersec2 B A k a line p A O perp q A p parallel r M p intersec E r q prove { equal { segment M E } { segment M D } } ','2008/01/09', '','gpreda1 ')
The Proof's code 0065 is correct.

Processing the XML file, please wait
/usr/local/bin/gclc proof0065.code proofCode0065.xml -xml > proof0065.errors
Warning: fopen(proof0065.xml.bz2) [function.fopen]: failed to open stream: No such file or directory in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 508

Warning: filesize() [function.filesize]: stat failed for proof0065.xml.bz2 in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 509

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INSERT INTO theorems (teoId,userId,category,description,shortDescription,teoName,dateSubmission) VALUES ('GEO0066','gpreda1 ','Geometry','\\begin{geothm} Let $G$ be a point on the circle $(O)$ with diameter $BC$, $A$ be the midpoint of the arc $BG$. $AD \\perp BC$. $E = AD \\cap BG$ and $F = AC \\cap BG$. Show that $AE \\cong BE \\cong EF$. \\end{geothm}',' ', ' Example 97 ','2008/01/09')

INSERT INTO bibtheorem (teoId,bibrefId) VALUES ('GEO0066','chou88')

INSERT INTO figures (teoId,drawerId,code,dateSubmission,bibref,userId) VALUES ('GEO0066','3',' dim 100 100 point B 10 50 point C 90 50 midpoint O B C circle k O B point G 55.30 89.65 med m B G intersec2 A A_1 k m line b B C perp d A b line g B G line o A O line c A C intersec E d g intersec D d b intersec M g o intersec F g c cmark_rb E cmark_l B cmark_r C cmark_b O cmark_b D cmark_b M cmark_lt A cmark_rt G cmark_t F drawcircle k drawsegment B C drawsegment B G drawsegment A D drawsegment A O drawsegment A C ','2008/01/09','chou88', 'gpreda1 ')
gclc figure0066.code figure0066.pic > figure0066.errors
Warning: fread() [function.fread]: Length parameter must be greater than 0 in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 328
Figura 520

    * Figure
    * figure0066.jpg
    * Description of the construction in natural language
    * figure0066.xml
    * Figure in SVG format
    * figure0066.svg

INSERT INTO demonstrations (teoId,proverId,code,dateSubmission,bibref,userId) VALUES ('GEO0066','2',' point B 10 50 point C 90 50 midpoint O B C circle k O B oncircle G O B med m B G intersec2 A A_1 k m line b B C perp d A b line g B G line c A C intersec E d g intersec D d b intersec F g c prove { equal { segment A E } { segment B E } } prove { equal { sratio B E E F } { 1 } } ','2008/01/09', '','gpreda1 ')
The Proof's code 0066 is correct.

Processing the XML file, please wait
/usr/local/bin/gclc proof0066.code proofCode0066.xml -xml > proof0066.errors
Warning: fopen(proof0066.xml.bz2) [function.fopen]: failed to open stream: No such file or directory in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 508

Warning: filesize() [function.filesize]: stat failed for proof0066.xml.bz2 in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 509

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INSERT INTO theorems (teoId,userId,category,description,shortDescription,teoName,dateSubmission) VALUES ('GEO0067','gpreda1 ','Geometry','\\begin{geothm} The two tangents to the circumcircle of $ABC$ at $A$ and $C$ meet at $E$. The mediator of $BC$ meet $AB$ at $D$. Show that $DE \\parallel BC$. \\end{geothm}',' ', ' Example 102 ','2008/01/09')

INSERT INTO bibtheorem (teoId,bibrefId) VALUES ('GEO0067','chou88')

INSERT INTO figures (teoId,drawerId,code,dateSubmission,bibref,userId) VALUES ('GEO0067','3',' dim 110 85 point A 35 25 point B 90 25 point C 58 68 med ma B C med mc A B intersec O ma mc circle k O A line a B C intersec H ma a line c A B intersec D ma c line ao A O line co C O perp pa A ao perp pc C co intersec E pa pc cmark_t E cmark_b D cmark_rb O drawcircle k cmark_b A cmark_b B cmark_t C cmark_rt H drawsegment A B drawsegment A C drawsegment C B drawsegment A O drawsegment C O drawsegment A E drawsegment C E drawsegment D H drawdashsegment D E ','2008/01/09','chou88', 'gpreda1 ')
gclc figure0067.code figure0067.pic > figure0067.errors
Warning: fread() [function.fread]: Length parameter must be greater than 0 in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 328
Figura 528

    * Figure
    * figure0067.jpg
    * Description of the construction in natural language
    * figure0067.xml
    * Figure in SVG format
    * figure0067.svg

INSERT INTO demonstrations (teoId,proverId,code,dateSubmission,bibref,userId) VALUES ('GEO0067','2',' point A 35 25 point B 90 25 point C 58 68 med ma B C med mc A B intersec O ma mc line a B C intersec H ma a line c A B intersec D ma c line ao A O line co C O perp pa A ao perp pc C co intersec E pa pc prove { parallel D E B C } ','2008/01/09', '','gpreda1 ')
The Proof's code 0067 is correct.

Processing the XML file, please wait
/usr/local/bin/gclc proof0067.code proofCode0067.xml -xml > proof0067.errors
Warning: fread() [function.fread]: Length parameter must be greater than 0 in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 497

INSERT INTO theorems (teoId,userId,category,description,shortDescription,teoName,dateSubmission) VALUES ('GEO0068','gpreda1 ','Geometry','\\begin{geothm} The product of two sides of a triangle is equal to the altitude to the third side multiplied by the circumdiameter. \\end{geothm}',' ', ' Example 140 ','2008/01/09')

INSERT INTO bibtheorem (teoId,bibrefId) VALUES ('GEO0068','chou88')

INSERT INTO figures (teoId,drawerId,code,dateSubmission,bibref,userId) VALUES ('GEO0068','3',' dim 110 110 point A 20 30 point B 90 30 point C 73 85 line c A B med mc B C med mb A C intersec O mc mb circle k O A foot F C c cmark_b F cmark_lb A cmark_rb B cmark_t C cmark_t O drawsegment A B drawsegment A C drawsegment C B drawsegment C F drawsegment A O drawcircle k ','2008/01/09','chou88', 'gpreda1 ')
gclc figure0068.code figure0068.pic > figure0068.errors
Warning: fread() [function.fread]: Length parameter must be greater than 0 in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 328
Figura 536

    * Figure
    * figure0068.jpg
    * Description of the construction in natural language
    * figure0068.xml
    * Figure in SVG format
    * figure0068.svg

INSERT INTO demonstrations (teoId,proverId,code,dateSubmission,bibref,userId) VALUES ('GEO0068','2',' point A 20 30 point B 90 30 point C 73 85 line c A B med mc B C med mb A C intersec O mc mb circle k O A foot F C c prove { equal { mult { segment A C } { segment B C } } { mult { 4 } { mult { segment O A } { segment C F } } } } ','2008/01/09', '','gpreda1 ')
The Proof's code 0068 is correct.

Processing the XML file, please wait
/usr/local/bin/gclc proof0068.code proofCode0068.xml -xml > proof0068.errors
Warning: fopen(proof0068.xml.bz2) [function.fopen]: failed to open stream: No such file or directory in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 508

Warning: filesize() [function.filesize]: stat failed for proof0068.xml.bz2 in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 509

Warning: fread(): supplied argument is not a valid stream resource in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 509

Warning: fclose(): supplied argument is not a valid stream resource in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 511

INSERT INTO theorems (teoId,userId,category,description,shortDescription,teoName,dateSubmission) VALUES ('GEO0069','gpreda1 ','Geometry','\\begin{geothm} The internal and external bisectors of an angle of a triangle pass through the ends of the circumdiameters which is a perpendicular to the side opposite the vertex considered. \\end{geothm}',' ', ' Example 138 ','2008/01/09')

INSERT INTO bibtheorem (teoId,bibrefId) VALUES ('GEO0069','chou88')

INSERT INTO figures (teoId,drawerId,code,dateSubmission,bibref,userId) VALUES ('GEO0069','3',' dim 110 110 point A 20 30 point B 90 30 point C 73 85 line c A B med mc B C med mb A C intersec O mc mb circle k O A perp l O c intersec2 L1 L l k cmark_lb A cmark_rb B cmark_t C cmark_t O cmark_b L drawsegment A B drawsegment A C drawsegment C B drawsegment O L drawsegment C L drawcircle k ','2008/01/09','chou88', 'gpreda1 ')
gclc figure0069.code figure0069.pic > figure0069.errors
Warning: fread() [function.fread]: Length parameter must be greater than 0 in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 328
Figura 544

    * Figure
    * figure0069.jpg
    * Description of the construction in natural language
    * figure0069.xml
    * Figure in SVG format
    * figure0069.svg

INSERT INTO demonstrations (teoId,proverId,code,dateSubmission,bibref,userId) VALUES ('GEO0069','2',' point A 20 30 point B 90 30 point C 73 85 line c A B med mc B C med mb A C intersec O mc mb circle k O A perp l O c intersec2 L1 L l k prove { equal { angle A C L } { angle L C B } } ','2008/01/09', '','gpreda1 ')
The Proof's code 0069 is correct.

Processing the XML file, please wait
/usr/local/bin/gclc proof0069.code proofCode0069.xml -xml > proof0069.errors
Warning: fopen(proof0069.xml.bz2) [function.fopen]: failed to open stream: No such file or directory in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 508

Warning: filesize() [function.filesize]: stat failed for proof0069.xml.bz2 in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 509

Warning: fread(): supplied argument is not a valid stream resource in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 509

Warning: fclose(): supplied argument is not a valid stream resource in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 511

INSERT INTO theorems (teoId,userId,category,description,shortDescription,teoName,dateSubmission) VALUES ('GEO0070','gpreda1 ','Geometry','\\begin{geothm} On the hypotenuse $AB$ of right triangle $ABC$ a square $ABFE$ is erected. Let $P$ be the intersection of the diagonals $AF$ and $BE$ of $ABFE$. Show that: $\\angle A C P = \\angle P C B$. \\end{geothm}',' ', ' Example 101 ','2008/01/09')

INSERT INTO bibtheorem (teoId,bibrefId) VALUES ('GEO0070','chou88')

INSERT INTO figures (teoId,drawerId,code,dateSubmission,bibref,userId) VALUES ('GEO0070','3',' dim 110 110 point C 40 30 point B 65 30 point A 40 65 line c A B perp f B c perp e A c circle k A B intersec2 E E_1 k e perp ef E e intersec F ef f line af A F line be B E intersec P af be perp ef1 E_1 e intersec F_1 ef1 f line af1 A F_1 line be1 B E_1 intersec P_1 af1 be1 cmark_lb C cmark_b B cmark_lt A cmark_t E cmark_rb F cmark_rb P cmark_t E_1 cmark_rb F_1 cmark_lb P_1 drawsegment A B drawsegment C B drawsegment A C drawsegment A E drawsegment A F drawsegment B F drawsegment E F drawsegment B E drawsegment C P drawdashsegment A E_1 drawdashsegment A F_1 drawdashsegment B F_1 drawdashsegment E_1 F_1 drawdashsegment B E_1 drawdashsegment C P_1 ','2008/01/09','chou88', 'gpreda1 ')
gclc figure0070.code figure0070.pic > figure0070.errors
Warning: fread() [function.fread]: Length parameter must be greater than 0 in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 328
Figura 552

    * Figure
    * figure0070.jpg
    * Description of the construction in natural language
    * figure0070.xml
    * Figure in SVG format
    * figure0070.svg

INSERT INTO demonstrations (teoId,proverId,code,dateSubmission,bibref,userId) VALUES ('GEO0070','2',' point C 40 30 point B 65 30 point A 40 65 line c A B perp f B c perp e A c circle k A B intersec2 E E_1 k e perp ef E e intersec F ef f line af A F line be B E intersec P af be prove { equal { angle A C P } { angle P C B } } ','2008/01/09', '','gpreda1 ')
The Proof's code 0070 is correct.

Processing the XML file, please wait
/usr/local/bin/gclc proof0070.code proofCode0070.xml -xml > proof0070.errors
Warning: fopen(proof0070.xml.bz2) [function.fopen]: failed to open stream: No such file or directory in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 508

Warning: filesize() [function.filesize]: stat failed for proof0070.xml.bz2 in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 509

Warning: fread(): supplied argument is not a valid stream resource in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 509

Warning: fclose(): supplied argument is not a valid stream resource in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 511

INSERT INTO theorems (teoId,userId,category,description,shortDescription,teoName,dateSubmission) VALUES ('GEO0071','gpreda1 ','Geometry','\\begin{geothm} A line parallel to the base of trapezoid $ABCD$ meet ifs two sides and two diagonals at $H$, $G$, $F$ and $E$. Show that: $EF \\cong GH$. \\end{geothm}',' ', ' Example 103 ','2008/01/09')

INSERT INTO bibtheorem (teoId,bibrefId) VALUES ('GEO0071','chou88')

INSERT INTO figures (teoId,drawerId,code,dateSubmission,bibref,userId) VALUES ('GEO0071','3',' dim 110 110 point A 20 20 point B 90 20 point D 45 90 point C 85 90 point H 31.95 53.46 line a A B parallel h H a line b B C intersec E h b line d B D line c C A intersec G c h intersec F d h cmark_b A cmark_b B cmark_t C cmark_t D cmark_l H cmark_r E cmark_rb G cmark_lb F drawsegment A B drawsegment C B drawsegment C D drawsegment A D drawsegment A C drawsegment B D drawsegment H E ','2008/01/09','chou88', 'gpreda1 ')
gclc figure0071.code figure0071.pic > figure0071.errors
Warning: fread() [function.fread]: Length parameter must be greater than 0 in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 328
Figura 560

    * Figure
    * figure0071.jpg
    * Description of the construction in natural language
    * figure0071.xml
    * Figure in SVG format
    * figure0071.svg

INSERT INTO demonstrations (teoId,proverId,code,dateSubmission,bibref,userId) VALUES ('GEO0071','2',' point A 20 20 point B 90 20 point D 45 90 point C 85 90 online H A D line a A B parallel h H a line b B C intersec E h b line d B D line c C A intersec G c h intersec F d h prove { equal { sratio H G F E } { 1 } } ','2008/01/09', '','gpreda1 ')
The Proof's code 0071 is correct.

Processing the XML file, please wait
/usr/local/bin/gclc proof0071.code proofCode0071.xml -xml > proof0071.errors
Warning: fread() [function.fread]: Length parameter must be greater than 0 in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 497

INSERT INTO theorems (teoId,userId,category,description,shortDescription,teoName,dateSubmission) VALUES ('GEO0072','gpreda1 ','Geometry','\\begin{geothm} Let $D$ and $E$ be two points on two sides $AC$ and $BC$ of triangle $ABC$ such that $AD \\cong BE$. $F = DE \\cap AB$. Show that: $FD \\cdot AC = EF \\cdot BC$. \\end{geothm}',' ', ' Example 110 ','2008/01/09')

INSERT INTO bibtheorem (teoId,bibrefId) VALUES ('GEO0072','chou88')

INSERT INTO figures (teoId,drawerId,code,dateSubmission,bibref,userId) VALUES ('GEO0072','3',' dim 120 110 point A 20 40 point B 85 40 point C 70 90 point D 40.26 60.26 line b A C parallel b1 B b line c A B parallel c1 D c intersec D1 b1 c1 line a B C circle k B D1 intersec2 E1 E k a line de D E intersec F de c cmark_lb A cmark_rb B cmark_t C cmark_lt D cmark_b E cmark_lb F drawsegment A B drawsegment C E drawsegment A C drawdashsegment B D1 drawdashsegment D D1 drawsegment D E ','2008/01/09','chou88', 'gpreda1 ')
gclc figure0072.code figure0072.pic > figure0072.errors
Warning: fread() [function.fread]: Length parameter must be greater than 0 in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 328
Figura 568

    * Figure
    * figure0072.jpg
    * Description of the construction in natural language
    * figure0072.xml
    * Figure in SVG format
    * figure0072.svg

INSERT INTO demonstrations (teoId,proverId,code,dateSubmission,bibref,userId) VALUES ('GEO0072','2',' point A 20 40 point B 85 40 point C 70 90 online D A C line b A C parallel b1 B b line c A B parallel c1 D c intersec D1 b1 c1 line a B C circle k B D1 intersec2 E1 E k a line de D E intersec F de c prove { equal { mult { segment F D } { segment A C } } { mult { segment E F } { segment B C } } } ','2008/01/09', '','gpreda1 ')
The Proof's code 0072 is correct.

Processing the XML file, please wait
/usr/local/bin/gclc proof0072.code proofCode0072.xml -xml > proof0072.errors
Warning: fopen(proof0072.xml.bz2) [function.fopen]: failed to open stream: No such file or directory in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 508

Warning: filesize() [function.filesize]: stat failed for proof0072.xml.bz2 in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 509

Warning: fread(): supplied argument is not a valid stream resource in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 509

Warning: fclose(): supplied argument is not a valid stream resource in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 511

INSERT INTO theorems (teoId,userId,category,description,shortDescription,teoName,dateSubmission) VALUES ('GEO0073','gpreda1 ','Geometry','\\begin{geothm} Two parallel line $AE$, $BD$ through the vertices $A$, $B$ of the triangle $ABC$ meet a line through the vertex $C$ in the points $E$, $D$. If the parallel through $E$ to $BC$ meets $AB$ in $F$, show that $DF$ is parallel to $AC$. \\end{geothm}',' ', ' Example 121 ','2008/01/09')

INSERT INTO bibtheorem (teoId,bibrefId) VALUES ('GEO0073','chou88')

INSERT INTO figures (teoId,drawerId,code,dateSubmission,bibref,userId) VALUES ('GEO0073','3',' dim 110 110 point A 20 35 point B 90 35 point C 70 90 point D 50 20 line bd B D parallel ae A bd line cd C D intersec E ae cd line bc B C parallel ef E bc line ab A B intersec F ab ef cmark_b A cmark_b B cmark_t C cmark_b D cmark_r E cmark_rb F drawsegment A B drawsegment C D drawsegment C B drawsegment A E drawsegment E F drawdashsegment A C drawdashsegment D F ','2008/01/09','chou88', 'gpreda1 ')
gclc figure0073.code figure0073.pic > figure0073.errors
Warning: fread() [function.fread]: Length parameter must be greater than 0 in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 328
Figura 576

    * Figure
    * figure0073.jpg
    * Description of the construction in natural language
    * figure0073.xml
    * Figure in SVG format
    * figure0073.svg

INSERT INTO demonstrations (teoId,proverId,code,dateSubmission,bibref,userId) VALUES ('GEO0073','2',' point A 20 35 point B 90 35 point C 70 90 point D 50 20 line bd B D parallel ae A bd line cd C D intersec E ae cd line bc B C parallel ef E bc line ab A B intersec F ab ef prove { parallel A C D F } ','2008/01/09', '','gpreda1 ')
The Proof's code 0073 is correct.

Processing the XML file, please wait
/usr/local/bin/gclc proof0073.code proofCode0073.xml -xml > proof0073.errors
Warning: fread() [function.fread]: Length parameter must be greater than 0 in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 497

INSERT INTO theorems (teoId,userId,category,description,shortDescription,teoName,dateSubmission) VALUES ('GEO0074','gpreda1 ','Geometry','\\begin{geothm} Let $C$ be the midpoint of the arc $AB$ of circle $(O)$. $D$ is a point on the circle. $E = AB \\cap CD$. Show that: $CA^2 = CE \\cdot CD$. \\end{geothm}',' ', ' Example 108 ','2008/01/09')

INSERT INTO bibtheorem (teoId,bibrefId) VALUES ('GEO0074','chou88')

INSERT INTO figures (teoId,drawerId,code,dateSubmission,bibref,userId) VALUES ('GEO0074','3',' dim 110 110 point A 20 30 point B 90 30 point X 25 34 line ab A B line ax A X med c A B intersec O c ax intersec M c ab circle k O A intersec2 C C1 k c point D 39.67 15.88 line cd C D intersec E ab cd cmark_lb A cmark_rb B cmark_t C cmark_r O cmark_b M cmark_lb D cmark_lt E drawcircle k drawsegment A B drawsegment C B drawsegment A C drawsegment C M drawsegment C D ','2008/01/09','chou88', 'gpreda1 ')
gclc figure0074.code figure0074.pic > figure0074.errors
Warning: fread() [function.fread]: Length parameter must be greater than 0 in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 328
Figura 584

    * Figure
    * figure0074.jpg
    * Description of the construction in natural language
    * figure0074.xml
    * Figure in SVG format
    * figure0074.svg

INSERT INTO demonstrations (teoId,proverId,code,dateSubmission,bibref,userId) VALUES ('GEO0074','2',' point A 20 30 point B 90 30 point X 25 34 line ab A B line ax A X med c A B intersec O c ax intersec M c ab circle k O A intersec2 C C1 k c oncircle D O A line cd C D intersec E ab cd prove { equal { mult { segment C A } { segment C A } } { mult { segment C E } { segment C D } } } ','2008/01/09', '','gpreda1 ')
The Proof's code 0074 is correct.

Processing the XML file, please wait
/usr/local/bin/gclc proof0074.code proofCode0074.xml -xml > proof0074.errors
Warning: fopen(proof0074.xml.bz2) [function.fopen]: failed to open stream: No such file or directory in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 508

Warning: filesize() [function.filesize]: stat failed for proof0074.xml.bz2 in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 509

Warning: fread(): supplied argument is not a valid stream resource in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 509

Warning: fclose(): supplied argument is not a valid stream resource in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 511

INSERT INTO theorems (teoId,userId,category,description,shortDescription,teoName,dateSubmission) VALUES ('GEO0075','gpreda1 ','Geometry','\\begin{geothm} Through point $F$ on the circle with diameter $AB$ a tangent to the circle is drawn meeting the two lines, perpendicular to $AB$ at $A$ and $B$, at $D$ and $E$. Show that: $OA^2 = DF \\cdot EF$. \\end{geothm}',' ', ' Example 114 ','2008/01/09')

INSERT INTO bibtheorem (teoId,bibrefId) VALUES ('GEO0075','chou88')

INSERT INTO figures (teoId,drawerId,code,dateSubmission,bibref,userId) VALUES ('GEO0075','3',' dim 110 110 point A 20 45 point B 90 45 midpoint O A B circle k O A point F 48.77 79.44 line ab A B line f F O perp de F f perp ad A ab perp be B ab intersec D ad de intersec E be de cmark_l A cmark_r B cmark_b O cmark_lt F cmark_t D cmark_t E drawsegment A B drawsegment O F drawsegment D E drawsegment E B drawsegment A D drawcircle k ','2008/01/09','chou88', 'gpreda1 ')
gclc figure0075.code figure0075.pic > figure0075.errors
Warning: fread() [function.fread]: Length parameter must be greater than 0 in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 328
Figura 592

    * Figure
    * figure0075.jpg
    * Description of the construction in natural language
    * figure0075.xml
    * Figure in SVG format
    * figure0075.svg

INSERT INTO demonstrations (teoId,proverId,code,dateSubmission,bibref,userId) VALUES ('GEO0075','2',' point A 20 45 point B 90 45 midpoint O A B circle k O A oncircle F O A line ab A B line f F O perp de F f perp ad A ab perp be B ab intersec D ad de intersec E be de prove { equal { mult { segment O A } { segment O A } } { mult { segment D F } { segment E F } } } ','2008/01/09', '','gpreda1 ')
The Proof's code 0075 is correct.

Processing the XML file, please wait
/usr/local/bin/gclc proof0075.code proofCode0075.xml -xml > proof0075.errors
Warning: fopen(proof0075.xml.bz2) [function.fopen]: failed to open stream: No such file or directory in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 508

Warning: filesize() [function.filesize]: stat failed for proof0075.xml.bz2 in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 509

Warning: fread(): supplied argument is not a valid stream resource in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 509

Warning: fclose(): supplied argument is not a valid stream resource in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 511

INSERT INTO theorems (teoId,userId,category,description,shortDescription,teoName,dateSubmission) VALUES ('GEO0076','gpreda1 ','Geometry','\\begin{geothm} From a point $A$ two lines are drawn tangent to circle $(O)$ at $B$ and $C$. From a point $P$ on the circle peprendiculars are drawn to $BC$, $AB$ and $AC$. Let $D$, $F$, $E$ be the feet. Show that: $PD^2 = PE \\cdot PF$. \\end{geothm}',' ', ' Example 117 ','2008/01/09')

INSERT INTO bibtheorem (teoId,bibrefId) VALUES ('GEO0076','chou88')

INSERT INTO figures (teoId,drawerId,code,dateSubmission,bibref,userId) VALUES ('GEO0076','3',' dim 110 90 point A 20 20 point B 70 20 line ab A B point X 60 70 line ac A X bis s B A X perp b B ab intersec O b s foot C O ac circle k O B point P 46.05 42.01 line bc B C foot F P ab foot E P ac foot D P bc cmark_b A cmark_b B cmark_rt O cmark_lt C cmark_rt D cmark_b F cmark_lt E cmark_lb P drawcircle k drawsegment A B drawsegment A C drawsegment O B drawsegment O C drawsegment C B drawsegment P F drawsegment P E drawsegment P D ','2008/01/09','chou88', 'gpreda1 ')
gclc figure0076.code figure0076.pic > figure0076.errors
Warning: fread() [function.fread]: Length parameter must be greater than 0 in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 328
Figura 600

    * Figure
    * figure0076.jpg
    * Description of the construction in natural language
    * figure0076.xml
    * Figure in SVG format
    * figure0076.svg

INSERT INTO demonstrations (teoId,proverId,code,dateSubmission,bibref,userId) VALUES ('GEO0076','2',' point A 20 20 point B 70 20 line ab A B point X 60 70 line ac A X bis s B A X perp b B ab intersec O b s foot C O ac circle k O B oncircle P O B line bc B C foot F P ab foot E P ac foot D P bc prove { equal { mult { segment P D } { segment P D } } { mult { segment P E } { segment P F } } } ','2008/01/09', '','gpreda1 ')
The Proof's code 0076 is correct.

Processing the XML file, please wait
/usr/local/bin/gclc proof0076.code proofCode0076.xml -xml > proof0076.errors
Warning: fopen(proof0076.xml.bz2) [function.fopen]: failed to open stream: No such file or directory in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 508

Warning: filesize() [function.filesize]: stat failed for proof0076.xml.bz2 in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 509

Warning: fread(): supplied argument is not a valid stream resource in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 509

Warning: fclose(): supplied argument is not a valid stream resource in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 511

INSERT INTO theorems (teoId,userId,category,description,shortDescription,teoName,dateSubmission) VALUES ('GEO0077','gpreda1 ','Geometry','\\begin{geothm} Of $Q$, $R$ are the projections of a point $M$ of the internal bisector $AM$ of the angle $A$ of the triangle $ABC$ upon the sides $AC$, $AB$, show that the perpendicular $MP$ from $M$ upon $BC$ meets $QR$ in the point $N$ on the median $AA_1$ of $ABC$. \\end{geothm}',' ', ' Example 127 ','2008/01/09')

INSERT INTO bibtheorem (teoId,bibrefId) VALUES ('GEO0077','chou88')

INSERT INTO figures (teoId,drawerId,code,dateSubmission,bibref,userId) VALUES ('GEO0077','3',' dim 150 110 point A 65 20 point B 120 20 point C 50 90 line a C B bis s B A C intersec X s a point M 102.91 66.89 line b A C line c A B foot Q M b foot R M c midpoint A_1 B C line a1 A A_1 line qr Q R intersec N qr a1 point B1 10 20 bis s1 B1 A C point M_1 48.20 33.60 foot Q_1 M_1 b foot R_1 M_1 c line qr1 Q_1 R_1 intersec N_1 qr1 a1 cmark_b A cmark_b B cmark_l C cmark_t M cmark_lb Q cmark_b R cmark_rt A_1 cmark_t N cmark_lt M_1 cmark_r Q_1 cmark_b R_1 cmark_t N_1 drawsegment R_1 B drawsegment C B drawsegment A C drawsegment A A_1 drawsegment M N drawsegment M Q drawsegment A M drawsegment M R drawdashsegment Q R drawdashsegment M_1 N_1 drawdashsegment M_1 Q_1 drawdashsegment A M_1 drawdashsegment M_1 R_1 drawdashsegment N_1 R_1 ','2008/01/09','chou88', 'gpreda1 ')
gclc figure0077.code figure0077.pic > figure0077.errors
Warning: fread() [function.fread]: Length parameter must be greater than 0 in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 328
Figura 608

    * Figure
    * figure0077.jpg
    * Description of the construction in natural language
    * figure0077.xml
    * Figure in SVG format
    * figure0077.svg

INSERT INTO demonstrations (teoId,proverId,code,dateSubmission,bibref,userId) VALUES ('GEO0077','2',' point A 65 20 point B 120 20 point C 50 90 line a C B bis s B A C intersec X s a online M A X line b A C line c A B foot Q M b foot R M c midpoint A_1 B C line a1 A A_1 line qr Q R intersec N qr a1 prove { perpendicular B C M N } ','2008/01/09', '','gpreda1 ')
The Proof's code 0077 is correct.

Processing the XML file, please wait
/usr/local/bin/gclc proof0077.code proofCode0077.xml -xml > proof0077.errors
Warning: fread() [function.fread]: Length parameter must be greater than 0 in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 497

INSERT INTO theorems (teoId,userId,category,description,shortDescription,teoName,dateSubmission) VALUES ('GEO0078','gpreda1 ','Geometry','\\begin{geothm} If $M$, $N$ are points on the sides $AC$, $BC$ of a triangle $ABC$ and the lines $AN$, $BM$ intersect on the altitude $CD$, show that $CD$ is the bisector of the angle $\\angle MDN$. \\end{geothm}',' ', ' Example 133 ','2008/01/09')

INSERT INTO bibtheorem (teoId,bibrefId) VALUES ('GEO0078','chou88')

INSERT INTO figures (teoId,drawerId,code,dateSubmission,bibref,userId) VALUES ('GEO0078','3',' dim 110 110 point A 20 20 point B 90 20 point C 70 80 line c A B line a B C line b A C foot D C c point J 70 50 line aj A J line bj B J intersec M bj b intersec N aj a cmark_b A cmark_b B cmark_t C cmark_lt M cmark_rt N cmark_b D cmark_lb J drawsegment A B drawsegment A C drawsegment C B drawsegment C D drawsegment M B drawsegment A N drawsegment D M drawsegment D N ','2008/01/09','chou88', 'gpreda1 ')
gclc figure0078.code figure0078.pic > figure0078.errors
Warning: fread() [function.fread]: Length parameter must be greater than 0 in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 328
Figura 616

    * Figure
    * figure0078.jpg
    * Description of the construction in natural language
    * figure0078.xml
    * Figure in SVG format
    * figure0078.svg

INSERT INTO demonstrations (teoId,proverId,code,dateSubmission,bibref,userId) VALUES ('GEO0078','2',' point A 20 20 point B 90 20 point C 70 80 line c A B line a B C line b A C foot D C c online J C D line aj A J line bj B J intersec M bj b intersec N aj a prove { equal { angle M D C } { angle C D N } } ','2008/01/09', '','gpreda1 ')
The Proof's code 0078 is correct.

Processing the XML file, please wait
/usr/local/bin/gclc proof0078.code proofCode0078.xml -xml > proof0078.errors
Warning: fopen(proof0078.xml.bz2) [function.fopen]: failed to open stream: No such file or directory in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 508

Warning: filesize() [function.filesize]: stat failed for proof0078.xml.bz2 in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 509

Warning: fread(): supplied argument is not a valid stream resource in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 509

Warning: fclose(): supplied argument is not a valid stream resource in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 511

INSERT INTO theorems (teoId,userId,category,description,shortDescription,teoName,dateSubmission) VALUES ('GEO0079','gpreda1 ','Geometry','\\begin{geothm} Show that the internal (or external) bisector of an angle of a triangle is divided harmonically by the feet of the perpendiculars dropped upon it from the two other vertices of the triangle. \\end{geothm}',' ', ' Example 136 ','2008/01/09')

INSERT INTO bibtheorem (teoId,bibrefId) VALUES ('GEO0079','chou88')

INSERT INTO figures (teoId,drawerId,code,dateSubmission,bibref,userId) VALUES ('GEO0079','3',' dim 110 110 point A 20 30 point B 90 30 point C 70 80 line c A B bis s A C B foot K B s foot J A s intersec F c s towards A_1 A C 2 bis s_1 A_1 C B foot K_1 B s_1 foot J_1 A s_1 intersec F_1 c s_1 cmark_b A cmark_b B cmark_t C cmark_rb F cmark_rb J cmark_l K cmark_rb F_1 cmark_t J_1 cmark_t K_1 drawsegment A B drawsegment A C drawsegment C B drawsegment C J drawsegment B K drawsegment A J drawdashsegment F_1 J_1 drawdashsegment B K_1 drawdashsegment A J_1 drawdashsegment C A_1 ','2008/01/09','chou88', 'gpreda1 ')
gclc figure0079.code figure0079.pic > figure0079.errors
Warning: fread() [function.fread]: Length parameter must be greater than 0 in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 328
Figura 624

    * Figure
    * figure0079.jpg
    * Description of the construction in natural language
    * figure0079.xml
    * Figure in SVG format
    * figure0079.svg

INSERT INTO demonstrations (teoId,proverId,code,dateSubmission,bibref,userId) VALUES ('GEO0079','2',' point A 20 30 point B 90 30 point C 70 80 line c A B bis s A C B foot K B s foot J A s intersec F c s prove { harmonic C F J K } ','2008/01/09', '','gpreda1 ')
The Proof's code 0079 is correct.

Processing the XML file, please wait
/usr/local/bin/gclc proof0079.code proofCode0079.xml -xml > proof0079.errors
Warning: fopen(proof0079.xml.bz2) [function.fopen]: failed to open stream: No such file or directory in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 508

Warning: filesize() [function.filesize]: stat failed for proof0079.xml.bz2 in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 509

Warning: fread(): supplied argument is not a valid stream resource in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 509

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INSERT INTO theorems (teoId,userId,category,description,shortDescription,teoName,dateSubmission) VALUES ('GEO0080','gpreda1 ','Geometry','\\begin{geothm} The angle between the circumdiameter and the altitude issued from the same vertex of a triangle is bisected by the bisector of angle of the triangle at the same vertex considered. \\end{geothm}',' ', ' Example 137 ','2008/01/09')

INSERT INTO bibtheorem (teoId,bibrefId) VALUES ('GEO0080','chou88')

INSERT INTO figures (teoId,drawerId,code,dateSubmission,bibref,userId) VALUES ('GEO0080','3',' dim 110 110 point A 20 30 point B 90 30 point C 73 85 line c A B med mc B C med mb A C intersec O mc mb bis s A C B intersec F s c foot D C c circle k O A towards A_1 A C 2 bis s1 A_1 C B drawdashline s1 towards O_1 O C 2 drawdashsegment C O_1 cmark_lb A cmark_rb B cmark_t C cmark_b F cmark_b D cmark_b O drawsegment A B drawsegment A C drawsegment C B drawsegment C D drawsegment C F drawsegment C O drawcircle k ','2008/01/09','chou88', 'gpreda1 ')
gclc figure0080.code figure0080.pic > figure0080.errors
Warning: fread() [function.fread]: Length parameter must be greater than 0 in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 328
Figura 632

    * Figure
    * figure0080.jpg
    * Description of the construction in natural language
    * figure0080.xml
    * Figure in SVG format
    * figure0080.svg

INSERT INTO demonstrations (teoId,proverId,code,dateSubmission,bibref,userId) VALUES ('GEO0080','2',' point A 20 30 point B 90 30 point C 73 85 line c A B med mc B C med mb A C intersec O mc mb bis s A C B intersec F s c foot D C c circle k O A prove { equal { angle O C F } { angle F C D } } ','2008/01/09', '','gpreda1 ')
The Proof's code 0080 is correct.

Processing the XML file, please wait
/usr/local/bin/gclc proof0080.code proofCode0080.xml -xml > proof0080.errors
Warning: fopen(proof0080.xml.bz2) [function.fopen]: failed to open stream: No such file or directory in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 508

Warning: filesize() [function.filesize]: stat failed for proof0080.xml.bz2 in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 509

Warning: fread(): supplied argument is not a valid stream resource in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 509

Warning: fclose(): supplied argument is not a valid stream resource in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 511

INSERT INTO theorems (teoId,userId,category,description,shortDescription,teoName,dateSubmission) VALUES ('GEO0081','gpreda1 ','Geometry','\\begin{geothm} The area of a triangle is equal to the product of its three sides divided by the double circumdiameter of the triangle. \\end{geothm}',' ', ' Example 141 ','2008/01/09')

INSERT INTO bibtheorem (teoId,bibrefId) VALUES ('GEO0081','chou88')

INSERT INTO figures (teoId,drawerId,code,dateSubmission,bibref,userId) VALUES ('GEO0081','3',' dim 110 110 point A 20 30 point B 90 30 point C 73 85 line c A B med mc B C med mb A C intersec O mc mb circle k O A cmark_lb A cmark_rb B cmark_t C cmark_t O drawsegment A B drawsegment A C drawsegment C B drawsegment A O drawcircle k ','2008/01/09','chou88', 'gpreda1 ')
gclc figure0081.code figure0081.pic > figure0081.errors
Warning: fread() [function.fread]: Length parameter must be greater than 0 in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 328
Figura 640

    * Figure
    * figure0081.jpg
    * Description of the construction in natural language
    * figure0081.xml
    * Figure in SVG format
    * figure0081.svg

INSERT INTO demonstrations (teoId,proverId,code,dateSubmission,bibref,userId) VALUES ('GEO0081','2',' point A 20 30 point B 90 30 point C 73 85 line c A B med mc B C med mb A C intersec O mc mb circle k O A prove { equal { mult { 16 } { mult { signed_area3 A B C } { mult { signed_area3 A B C } { segment A O } } } } { mult { segment A B } { mult { segment A C } { segment B C } } } } } ','2008/01/09', '','gpreda1 ')
The Proof's code 0081 is correct.

Processing the XML file, please wait
/usr/local/bin/gclc proof0081.code proofCode0081.xml -xml > proof0081.errors
Warning: fopen(proof0081.xml.bz2) [function.fopen]: failed to open stream: No such file or directory in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 508

Warning: filesize() [function.filesize]: stat failed for proof0081.xml.bz2 in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 509

Warning: fread(): supplied argument is not a valid stream resource in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 509

Warning: fclose(): supplied argument is not a valid stream resource in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 511

INSERT INTO theorems (teoId,userId,category,description,shortDescription,teoName,dateSubmission) VALUES ('GEO0082','gpreda1 ','Geometry','\\begin{geothm} Let $M$ be the midpoint of chord $AB$ of a circle with center $O$. On $OM$ as diameter draw another circle, and at any point $T$ of this circle draw a tangent to it meeting the outer circle in $E$. Prove that: $AE^2 + BE^2 = 4ET^2$. \\end{geothm}',' ', ' Example 132 ','2008/01/09')

INSERT INTO bibtheorem (teoId,bibrefId) VALUES ('GEO0082','chou88')

INSERT INTO figures (teoId,drawerId,code,dateSubmission,bibref,userId) VALUES ('GEO0082','3',' dim 110 110 point A 30 30 point B 80 30 med m A B point X 35 34 line ax A X intersec O ax m line ab A B intersec M m ab circle k O A midpoint N O M circle k1 N M point T 45.46 37.01 line tn T N perp t T tn intersec2 E E1 t k cmark_lb A cmark_rb B cmark_lt O cmark_b M cmark_r N cmark_lb T cmark_lt E drawsegment A B drawsegment A E drawsegment E B drawsegment O M drawsegment T E drawsegment T N drawcircle k drawcircle k1 ','2008/01/09','chou88', 'gpreda1 ')
gclc figure0082.code figure0082.pic > figure0082.errors
Warning: fread() [function.fread]: Length parameter must be greater than 0 in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 328
Figura 648

    * Figure
    * figure0082.jpg
    * Description of the construction in natural language
    * figure0082.xml
    * Figure in SVG format
    * figure0082.svg

INSERT INTO demonstrations (teoId,proverId,code,dateSubmission,bibref,userId) VALUES ('GEO0082','2',' point A 30 30 point B 80 30 med m A B point X 35 34 line ax A X intersec O ax m line ab A B intersec M m ab circle k O A midpoint N O M circle k1 N M oncircle T N M line tn T N perp t T tn intersec2 E E1 t k prove { equal { mult { 4 } { segment E T } } { sum { segment A E } { segment B E } } } ','2008/01/09', '','gpreda1 ')
The Proof's code 0082 is correct.

Processing the XML file, please wait
/usr/local/bin/gclc proof0082.code proofCode0082.xml -xml > proof0082.errors
Warning: fopen(proof0082.xml.bz2) [function.fopen]: failed to open stream: No such file or directory in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 508

Warning: filesize() [function.filesize]: stat failed for proof0082.xml.bz2 in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 509

Warning: fread(): supplied argument is not a valid stream resource in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 509

Warning: fclose(): supplied argument is not a valid stream resource in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 511

INSERT INTO theorems (teoId,userId,category,description,shortDescription,teoName,dateSubmission) VALUES ('GEO0083','gpreda1 ','Geometry','\\begin{geothm} Line $p$ intersects lines $AB$, $BC$, $CD$ and $DA$ at points $A_1$, $B_1$, $C_1$ and $D_1$ respectively. Show that: $\\frac{\\overline{AA_1}}{\\overline{A_1B}} \\cdot \\frac{\\overline{BB_1}}{\\overline{B_1C}} \\cdot \\frac{\\overline{CC_1}}{\\overline{C_1D}} \\cdot \\frac{\\overline{DD_1}}{\\overline{D_1A}} \\cdot = 1$ \\end{geothm}',' ', ' General Menelaus s Theorem ','2008/01/09')

INSERT INTO bibtheorem (teoId,bibrefId) VALUES ('GEO0082','chou88')

INSERT INTO figures (teoId,drawerId,code,dateSubmission,bibref,userId) VALUES ('GEO0083','3',' dim 100 100 point A 20 20 point B 80 20 point C 70 60 point D 37 74 line ab A B line bc B C line da D A line cd C D point A_1 85 20 point B_1 77.5 32.5 line a1b1 A_1 B_1 intersec C_1 a1b1 cd intersec D_1 a1b1 da cmark_rb A cmark_b B cmark_r C cmark_l D cmark_rt A_1 cmark_r B_1 cmark_rt C_1 cmark_r D_1 drawsegment A B drawsegment C B drawsegment C D drawsegment A D drawdashline a1b1 drawline da drawline ab ','2008/01/09','', 'gpreda1 ')
gclc figure0083.code figure0083.pic > figure0083.errors
Warning: fread() [function.fread]: Length parameter must be greater than 0 in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 328
Figura 656

    * Figure
    * figure0083.jpg
    * Description of the construction in natural language
    * figure0083.xml
    * Figure in SVG format
    * figure0083.svg

INSERT INTO demonstrations (teoId,proverId,code,dateSubmission,bibref,userId) VALUES ('GEO0083','2',' point A 20 20 point B 80 20 point C 70 60 point D 37 74 line ab A B line bc B C line da D A line cd C D online A_1 A B online B_1 B C line a1b1 A_1 B_1 intersec C_1 a1b1 cd intersec D_1 a1b1 da prove { equal { mult { mult { mult { sratio A A_1 A_1 B } { sratio B B_1 B_1 C } } { sratio C C_1 C_1 D } } { sratio D D_1 D_1 A } } 1 } ','2008/01/09', '','gpreda1 ')
The Proof's code 0083 is correct.

Processing the XML file, please wait
/usr/local/bin/gclc proof0083.code proofCode0083.xml -xml > proof0083.errors
Warning: fread() [function.fread]: Length parameter must be greater than 0 in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 497

INSERT INTO theorems (teoId,userId,category,description,shortDescription,teoName,dateSubmission) VALUES ('GEO0084','gpreda1 ','Geometry','\\begin{geothm} Let $ABC$ and $A_1B_1C_1$ be two lines such that $AB_1 \\parallel BA_1$ and $BC_1 \\parallel CB_1$. Show that $AC_1 \\parallel CA_1$. \\end{geothm}',' ', ' Pappus Theorem ','2008/01/09')

INSERT INTO bibtheorem (teoId,bibrefId) VALUES ('GEO0082','chou88')

INSERT INTO figures (teoId,drawerId,code,dateSubmission,bibref,userId) VALUES ('GEO0084','3',' dim 100 100 point A 20 10 point B 90 10 point C 50 10 cmark_b A cmark_b B cmark_b C point A_1 55 50 point A_2 45 43 line A_1A_2 A_1 A_2 line A_1B A_1 B parallel AB_1 A A_1B intersec B_1 A_1A_2 AB_1 line CB_1 C B_1 parallel BC_1 B CB_1 intersec C_1 A_1A_2 BC_1 cmark_lt A_1 cmark_lt B_1 cmark_lt C_1 drawline A C drawline A_1 C_1 drawsegment A B_1 drawsegment B A_1 drawsegment B C_1 drawsegment C B_1 drawsegment A C_1 drawsegment C A_1 ','2008/01/09','', 'gpreda1 ')
gclc figure0084.code figure0084.pic > figure0084.errors
Warning: fread() [function.fread]: Length parameter must be greater than 0 in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 328
Figura 664

    * Figure
    * figure0084.jpg
    * Description of the construction in natural language
    * figure0084.xml
    * Figure in SVG format
    * figure0084.svg

INSERT INTO demonstrations (teoId,proverId,code,dateSubmission,bibref,userId) VALUES ('GEO0084','2',' point A 20 10 point B 90 10 online C A B point A_1 55 50 point A_2 45 43 line A_1A_2 A_1 A_2 line A_1B A_1 B parallel AB_1 A A_1B intersec B_1 A_1A_2 AB_1 line CB_1 C B_1 parallel BC_1 B CB_1 intersec C_1 A_1A_2 BC_1 prove { parallel A_1 C A C_1 } ','2008/01/09', '','gpreda1 ')
The Proof's code 0084 is correct.

Processing the XML file, please wait
/usr/local/bin/gclc proof0084.code proofCode0084.xml -xml > proof0084.errors
Warning: fread() [function.fread]: Length parameter must be greater than 0 in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 497

INSERT INTO theorems (teoId,userId,category,description,shortDescription,teoName,dateSubmission) VALUES ('GEO0085','gpreda1 ','Geometry','\\begin{geothm} Let $ABC$ and $A_1B_1C_1$ be two lines and $P = AB_1 \\cap A_1B$, $Q = AC_1 \\cap A_1C$, $S = BC_1 \\cap B_1C$. Then $P$, $Q$ and $S$ are collinear. \\end{geothm}',' ', ' Pappus Theorem (second version) ','2008/01/09')

INSERT INTO bibtheorem (teoId,bibrefId) VALUES ('GEO0082','chou88')

INSERT INTO figures (teoId,drawerId,code,dateSubmission,bibref,userId) VALUES ('GEO0085','3',' dim 100 100 point A 20 20 point B 50 20 point C 77 20 point A_1 25 50 point B_1 52 60 point C_1 65.50 65.00 line ab1 A B_1 line ba1 B A_1 intersec P ab1 ba1 line ac1 A C_1 line ca1 C A_1 intersec Q ac1 ca1 line bc1 B C_1 line cb1 C B_1 intersec S bc1 cb1 line p A B line q A_1 B_1 line r P Q cmark_b A cmark_b B cmark_b C cmark_t A_1 cmark_t B_1 cmark_t C_1 cmark_b P cmark_b Q cmark_r S drawline p drawline q drawdashline r drawsegment A B_1 drawsegment A_1 B drawsegment A C_1 drawsegment A_1 C drawsegment C B_1 drawsegment C_1 B ','2008/01/09','', 'gpreda1 ')
gclc figure0085.code figure0085.pic > figure0085.errors
Warning: fread() [function.fread]: Length parameter must be greater than 0 in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 328
Figura 672

    * Figure
    * figure0085.jpg
    * Description of the construction in natural language
    * figure0085.xml
    * Figure in SVG format
    * figure0085.svg

INSERT INTO demonstrations (teoId,proverId,code,dateSubmission,bibref,userId) VALUES ('GEO0085','2',' point A 20 20 point B 50 20 point C 77 20 point A_1 25 50 point B_1 52 60 online C_1 A_1 B_1 line ab1 A B_1 line ba1 B A_1 intersec P ab1 ba1 line ac1 A C_1 line ca1 C A_1 intersec Q ac1 ca1 line bc1 B C_1 line cb1 C B_1 intersec S bc1 cb1 line p A B line q A_1 B_1 line r P Q prove { collinear P Q S } ','2008/01/09', '','gpreda1 ')
The Proof's code 0085 is correct.

Processing the XML file, please wait
/usr/local/bin/gclc proof0085.code proofCode0085.xml -xml > proof0085.errors
Warning: fread() [function.fread]: Length parameter must be greater than 0 in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 497

INSERT INTO theorems (teoId,userId,category,description,shortDescription,teoName,dateSubmission) VALUES ('GEO0086','gpreda1 ','Geometry','\\begin{geothm} Show that the distance of a point on a median of triangle from the sides including the median are inversely proportional to these sides, ie: $NK : NJ = BC : AC$. \\end{geothm}',' ', ' Example 145 ','2008/01/09')

INSERT INTO bibtheorem (teoId,bibrefId) VALUES ('GEO0086','chou88')

INSERT INTO figures (teoId,drawerId,code,dateSubmission,bibref,userId) VALUES ('GEO0086','3',' dim 110 110 point A 20 30 point B 90 30 point C 40 88 midpoint F A B line a B C line b A C point N 49.18 52.51 foot K N b foot J N a cmark_lb A cmark_rb B cmark_t C cmark_b F cmark_lt K cmark_rt J cmark_lb N drawsegment A B drawsegment A C drawsegment C B drawsegment C F drawsegment N K drawsegment N J ','2008/01/09','chou88', 'gpreda1 ')
gclc figure0086.code figure0086.pic > figure0086.errors
Warning: fread() [function.fread]: Length parameter must be greater than 0 in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 328
Figura 680

    * Figure
    * figure0086.jpg
    * Description of the construction in natural language
    * figure0086.xml
    * Figure in SVG format
    * figure0086.svg

INSERT INTO demonstrations (teoId,proverId,code,dateSubmission,bibref,userId) VALUES ('GEO0086','2',' point A 20 30 point B 90 30 point C 40 88 midpoint F A B line a B C line b A C online N C F foot K N b foot J N a prove { equal { mult { segment N K } { segment A C } } { mult { segment N J } { segment B C } } } ','2008/01/09', '','gpreda1 ')
The Proof's code 0086 is correct.

Processing the XML file, please wait
/usr/local/bin/gclc proof0086.code proofCode0086.xml -xml > proof0086.errors
Warning: fopen(proof0086.xml.bz2) [function.fopen]: failed to open stream: No such file or directory in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 508

Warning: filesize() [function.filesize]: stat failed for proof0086.xml.bz2 in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 509

Warning: fread(): supplied argument is not a valid stream resource in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 509

Warning: fclose(): supplied argument is not a valid stream resource in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 511

INSERT INTO theorems (teoId,userId,category,description,shortDescription,teoName,dateSubmission) VALUES ('GEO0087','gpreda1 ','Geometry','\\begin{geothm} If $G$ is a centroid of triangle $ABC$, show that for any given point $M$: $3 \\cdot MG^2 + AG^2 + BG^2 + CG^2 = AM^2 + BM^2 + CM^2$. \\end{geothm}',' ', ' Example 150 ','2008/01/09')

INSERT INTO bibtheorem (teoId,bibrefId) VALUES ('GEO0087','chou88')

INSERT INTO figures (teoId,drawerId,code,dateSubmission,bibref,userId) VALUES ('GEO0087','3',' dim 110 110 point A 20 30 point B 90 30 point C 40 88 point M 93 90 midpoint F A B midpoint E A C midpoint D B C line cf C F line ad A D intersec G ad cf cmark_lb A cmark_rb B cmark_t C cmark_t M cmark_lt G cmark_b F cmark_lt E cmark_rt D drawsegment A B drawsegment A C drawsegment C B drawsegment M B drawsegment C M drawsegment C F drawsegment A D drawsegment B E drawsegment G M ','2008/01/09','chou88', 'gpreda1 ')
gclc figure0087.code figure0087.pic > figure0087.errors
Warning: fread() [function.fread]: Length parameter must be greater than 0 in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 328
Figura 688

    * Figure
    * figure0087.jpg
    * Description of the construction in natural language
    * figure0087.xml
    * Figure in SVG format
    * figure0087.svg

INSERT INTO demonstrations (teoId,proverId,code,dateSubmission,bibref,userId) VALUES ('GEO0087','2',' point A 20 30 point B 90 30 point C 40 88 point M 93 90 midpoint F A B midpoint E A C midpoint D B C line cf C F line ad A D intersec G ad cf prove { equal { sum { mult { segment M G } { 3 } } { sum { segment A G } { sum { segment C G } { segment B G } } } } { sum { segment A M } { sum { segment B M } { segment C M } } } } ','2008/01/09', '','gpreda1 ')
The Proof's code 0087 is correct.

Processing the XML file, please wait
/usr/local/bin/gclc proof0087.code proofCode0087.xml -xml > proof0087.errors
Warning: fopen(proof0087.xml.bz2) [function.fopen]: failed to open stream: No such file or directory in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 508

Warning: filesize() [function.filesize]: stat failed for proof0087.xml.bz2 in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 509

Warning: fread(): supplied argument is not a valid stream resource in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 509

Warning: fclose(): supplied argument is not a valid stream resource in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 511

INSERT INTO theorems (teoId,userId,category,description,shortDescription,teoName,dateSubmission) VALUES ('GEO0088','gpreda1 ','Geometry','\\begin{geothm} Two tritangent centers divide the bisector on which they are located, harmonically (ie, points $C$, $D$, $I$ and $I_c$ are harmonic). \\end{geothm}',' ', ' Example 155 ','2008/01/09')

INSERT INTO bibtheorem (teoId,bibrefId) VALUES ('GEO0088','chou88')

INSERT INTO figures (teoId,drawerId,code,dateSubmission,bibref,userId) VALUES ('GEO0088','3',' dim 120 110 point A 20 63 point B 85 63 point C 28 98 bis sc A C B bis sa B A C perp sa_1 A sa line c A B intersec I sa sc intersec I_c sa_1 sc intersec D sc c foot X I c foot Y I_c c circle k I X circle k1 I_c Y towards A1 C A 10 towards B1 C B 10 drawdashsegment A A1 drawdashsegment B B1 drawdashcircle k drawdashcircle k1 cmark_lt A cmark_rt B cmark_t C cmark_rt I cmark_lb D cmark_rt I_c drawsegment A C drawsegment C B drawsegment A B drawsegment C I_c drawsegment A I drawsegment B I drawsegment A I_c ','2008/01/09','chou88', 'gpreda1 ')
gclc figure0088.code figure0088.pic > figure0088.errors
Warning: fread() [function.fread]: Length parameter must be greater than 0 in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 328
Figura 696

    * Figure
    * figure0088.jpg
    * Description of the construction in natural language
    * figure0088.xml
    * Figure in SVG format
    * figure0088.svg

INSERT INTO demonstrations (teoId,proverId,code,dateSubmission,bibref,userId) VALUES ('GEO0088','2',' point A 20 63 point B 85 63 point C 28 98 bis sc A C B bis sa B A C perp sa_1 A sa line c A B intersec I sa sc intersec I_c sa_1 sc intersec D sc c prove { harmonic C D I I_c } ','2008/01/09', '','gpreda1 ')
The Proof's code 0088 is correct.

Processing the XML file, please wait
/usr/local/bin/gclc proof0088.code proofCode0088.xml -xml > proof0088.errors
Warning: fopen(proof0088.xml.bz2) [function.fopen]: failed to open stream: No such file or directory in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 508

Warning: filesize() [function.filesize]: stat failed for proof0088.xml.bz2 in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 509

Warning: fread(): supplied argument is not a valid stream resource in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 509

Warning: fclose(): supplied argument is not a valid stream resource in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 511

INSERT INTO theorems (teoId,userId,category,description,shortDescription,teoName,dateSubmission) VALUES ('GEO0089','gpreda1 ','Geometry','\\begin{geothm} Show that in any given triangle the ratio between one triangle side and a diameter of circumscribed circle is equal to the sine of opposite angle, ie: $\\frac{a}{2R} = \\sin \\alpha$ \\end{geothm}',' ', ' Sine Theorem ','2008/01/09')

INSERT INTO bibtheorem (teoId,bibrefId) VALUES ('GEO0088','chou88')

INSERT INTO figures (teoId,drawerId,code,dateSubmission,bibref,userId) VALUES ('GEO0089','3',' dim 110 110 point A 20 30 point B 90 30 point C 70 90 med mc A B med mb A C intersec O mc mb circle k O A line c A B foot D C c cmark_b A cmark_b B cmark_t C cmark_b O drawcircle k cmark_b D drawsegment O C drawsegment C D drawsegment A B drawsegment C B drawsegment A C point a 83.00 58.40 printat a { a } point b 42.40 61.00 printat b { b } point c 57.90 28.20 printat c { c } point al 30.00 34.10 printat al { \\alpha } point r 60.00 70.90 printat r { R } point x 40 30 drawarc A x 50 point xx 41 30 drawarc A xx 50 ','2008/01/09','', 'gpreda1 ')
gclc figure0089.code figure0089.pic > figure0089.errors
Warning: fread() [function.fread]: Length parameter must be greater than 0 in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 328
Figura 704

    * Figure
    * figure0089.jpg
    * Description of the construction in natural language
    * figure0089.xml
    * Figure in SVG format
    * figure0089.svg

INSERT INTO demonstrations (teoId,proverId,code,dateSubmission,bibref,userId) VALUES ('GEO0089','2',' point A 20 30 point B 90 30 point C 70 90 med mc A B med mb A C intersec O mc mb circle k O A line c A B foot D C c prove { equal { mult { 4 } { mult { segment A O } { segment C D } } } { mult { segment B C } { segment C A } } } ','2008/01/09', '','gpreda1 ')
The Proof's code 0089 is correct.

Processing the XML file, please wait
/usr/local/bin/gclc proof0089.code proofCode0089.xml -xml > proof0089.errors
Warning: fopen(proof0089.xml.bz2) [function.fopen]: failed to open stream: No such file or directory in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 508

Warning: filesize() [function.filesize]: stat failed for proof0089.xml.bz2 in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 509

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INSERT INTO theorems (teoId,userId,category,description,shortDescription,teoName,dateSubmission) VALUES ('GEO0090','gpreda1 ','Geometry','\\begin{geothm} $c^2 + b^2 - 2bc \\cos \\alpha = a^2$ \\end{geothm}',' ', ' The Law of Cosine ','2008/01/09')

INSERT INTO bibtheorem (teoId,bibrefId) VALUES ('GEO0088','chou88')

INSERT INTO figures (teoId,drawerId,code,dateSubmission,bibref,userId) VALUES ('GEO0090','3',' dim 110 110 point A 20 30 point B 90 30 point C 70 90 line c A B foot D C c cmark_b A cmark_b B cmark_b D cmark_t C drawsegment C D drawsegment A B drawsegment C B drawsegment A C point a 83.00 58.40 printat a { a } point b 42.40 61.00 printat b { b } point c 57.90 28.20 printat c { c } point al 30.00 34.10 printat al { \\alpha } point x 40 30 drawarc A x 50 point xx 41 30 drawarc A xx 50 ','2008/01/09','', 'gpreda1 ')
gclc figure0090.code figure0090.pic > figure0090.errors
Warning: fread() [function.fread]: Length parameter must be greater than 0 in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 328
Figura 712

    * Figure
    * figure0090.jpg
    * Description of the construction in natural language
    * figure0090.xml
    * Figure in SVG format
    * figure0090.svg

INSERT INTO demonstrations (teoId,proverId,code,dateSubmission,bibref,userId) VALUES ('GEO0090','2',' point A 20 30 point B 90 30 point C 70 90 line c A B foot D C c prove { equal { mult { mult { sum { mult { -1 } { segment C B } } { sum { segment A C } { segment B A } } } { sum { mult { -1 } { segment C B } } { sum { segment A C } { segment B A } } } } { segment A C } } { mult { 4 } { mult { segment A C } { mult { segment B A } { segment A D } } } } } ','2008/01/09', '','gpreda1 ')
The Proof's code 0090 is correct.

Processing the XML file, please wait
/usr/local/bin/gclc proof0090.code proofCode0090.xml -xml > proof0090.errors
Warning: fopen(proof0090.xml.bz2) [function.fopen]: failed to open stream: No such file or directory in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 508

Warning: filesize() [function.filesize]: stat failed for proof0090.xml.bz2 in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 509

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Warning: fclose(): supplied argument is not a valid stream resource in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 511

INSERT INTO theorems (teoId,userId,category,description,shortDescription,teoName,dateSubmission) VALUES ('GEO0091','gpreda1 ','Geometry','\\begin{geothm} If $R$ and $r$ are half diameters of circumscribed and inscribed circles of a trougle and $d$ is a distance between them, show that: $d^2 = R(R - 2r)$. \\end{geothm}',' ', ' Euler s Formula ','2008/01/09')

INSERT INTO bibtheorem (teoId,bibrefId) VALUES ('GEO0088','chou88')

INSERT INTO figures (teoId,drawerId,code,dateSubmission,bibref,userId) VALUES ('GEO0091','3',' dim 105 90 point A 20 33 point B 85 33 point C 68 75 bis sc A C B bis sa B A C intersec I sa sc med mc A B med mb A C intersec O mc mb circle k O A line c A B foot D I c circle k1 I D drawcircle k1 drawcircle k cmark_b O cmark_lb A cmark_rb B cmark_t C cmark_rt I cmark_b D drawsegment A O drawsegment I D drawsegment A C drawsegment C B drawsegment A B drawdashsegment I O point x 56.00 48.00 printat x { d } point y 38.90 41.50 printat y { R } point z 63.30 41.30 printat z { r } ','2008/01/09','', 'gpreda1 ')
gclc figure0091.code figure0091.pic > figure0091.errors
Warning: fread() [function.fread]: Length parameter must be greater than 0 in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 328
Figura 720

    * Figure
    * figure0091.jpg
    * Description of the construction in natural language
    * figure0091.xml
    * Figure in SVG format
    * figure0091.svg

INSERT INTO demonstrations (teoId,proverId,code,dateSubmission,bibref,userId) VALUES ('GEO0091','2',' point A 20 33 point B 85 33 point C 68 75 bis sc A C B bis sa B A C intersec I sa sc med mc A B med mb A C intersec O mc mb circle k O A line c A B foot D I c circle k1 I D prove { equal { mult { sum { mult { -1 } { segment I O } } { segment A O } } { sum { mult { -1 } { segment I O } } { segment A O } } } { mult { 4 } { mult { segment A O } { segment I D } } } } ','2008/01/09', '','gpreda1 ')
The Proof's code 0091 is correct.

Processing the XML file, please wait
/usr/local/bin/gclc proof0091.code proofCode0091.xml -xml > proof0091.errors
Warning: fopen(proof0091.xml.bz2) [function.fopen]: failed to open stream: No such file or directory in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 508

Warning: filesize() [function.filesize]: stat failed for proof0091.xml.bz2 in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 509

Warning: fread(): supplied argument is not a valid stream resource in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 509

Warning: fclose(): supplied argument is not a valid stream resource in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 511

INSERT INTO theorems (teoId,userId,category,description,shortDescription,teoName,dateSubmission) VALUES ('GEO0092','gpreda1 ','Geometry','\\begin{geothm} Show that the area of a right triangle is equal to the product of the two segments into which the hypothenuse is divided by its point of contact with incircle. \\end{geothm}',' ', ' Example 172 ','2008/01/09')

INSERT INTO bibtheorem (teoId,bibrefId) VALUES ('GEO0092','chou88')

INSERT INTO figures (teoId,drawerId,code,dateSubmission,bibref,userId) VALUES ('GEO0092','3',' dim 90 90 point A 20 20 point B 70 20 line c A B point X 30 65 line x B X perp b A c intersec C x b bis sa B A C bis sb A B C intersec I sa sb line a B C foot D I a circle k I D drawcircle k cmark_rt D cmark_lt I cmark_b A cmark_b B cmark_t C drawsegment A C drawsegment C B drawsegment A B foot E I c foot F I b drawdashsegment I E drawdashsegment I F drawdashsegment I D ','2008/01/09','chou88', 'gpreda1 ')
gclc figure0092.code figure0092.pic > figure0092.errors
Warning: fread() [function.fread]: Length parameter must be greater than 0 in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 328
Figura 728

    * Figure
    * figure0092.jpg
    * Description of the construction in natural language
    * figure0092.xml
    * Figure in SVG format
    * figure0092.svg

INSERT INTO demonstrations (teoId,proverId,code,dateSubmission,bibref,userId) VALUES ('GEO0092','2',' point A 20 20 point B 70 20 line c A B point X 30 65 line x B X perp b A c intersec C x b bis sa B A C bis sb A B C intersec I sa sb line a B C foot D I a circle k I D prove { equal { mult { segment C D } { segment B D } } { mult { signed_area3 A B C } { signed_area3 A B C } } } ','2008/01/09', '','gpreda1 ')
The Proof's code 0092 is correct.

Processing the XML file, please wait
/usr/local/bin/gclc proof0092.code proofCode0092.xml -xml > proof0092.errors
Warning: fopen(proof0092.xml.bz2) [function.fopen]: failed to open stream: No such file or directory in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 508

Warning: filesize() [function.filesize]: stat failed for proof0092.xml.bz2 in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 509

Warning: fread(): supplied argument is not a valid stream resource in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 509

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INSERT INTO theorems (teoId,userId,category,description,shortDescription,teoName,dateSubmission) VALUES ('GEO0093','gpreda1 ','Geometry','\\begin{geothm} The segment of the altitude extended between the orthocenter and the second point of intersection with the circumcircle is bisected by the corresponding side of the triangle. \\end{geothm}',' ', ' Example 174 ','2008/01/09')

INSERT INTO bibtheorem (teoId,bibrefId) VALUES ('GEO0093','chou88')

INSERT INTO figures (teoId,drawerId,code,dateSubmission,bibref,userId) VALUES ('GEO0093','3',' dim 110 110 point A 20 30 point K 90 30 point D 70 30 line a A K perp c D a med o A K point X 24 33 line x A X intersec O o x circle k O A intersec2 C B c k line b A B foot E C b line hc C E intersec H hc a cmark_lt H drawsegment C E cmark_b E cmark_rt C drawcircle k cmark_b O cmark_lb A cmark_b B cmark_rb D cmark_rb K drawsegment A K drawsegment A B drawsegment A C drawsegment C B ','2008/01/09','chou88', 'gpreda1 ')
gclc figure0093.code figure0093.pic > figure0093.errors
Warning: fread() [function.fread]: Length parameter must be greater than 0 in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 328
Figura 736

    * Figure
    * figure0093.jpg
    * Description of the construction in natural language
    * figure0093.xml
    * Figure in SVG format
    * figure0093.svg

INSERT INTO demonstrations (teoId,proverId,code,dateSubmission,bibref,userId) VALUES ('GEO0093','2',' point A 20 30 point K 90 30 point D 70 30 line a A K perp c D a med o A K point X 24 33 line x A X intersec O o x circle k O A intersec2 C B c k line b A B foot E C b line hc C E intersec H hc a prove { equal { sratio H D D K } { 1 } } ','2008/01/09', '','gpreda1 ')
The Proof's code 0093 is correct.

Processing the XML file, please wait
/usr/local/bin/gclc proof0093.code proofCode0093.xml -xml > proof0093.errors
Warning: fread() [function.fread]: Length parameter must be greater than 0 in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 497

INSERT INTO theorems (teoId,userId,category,description,shortDescription,teoName,dateSubmission) VALUES ('GEO0094','gpreda1 ','Geometry','\\begin{geothm} Show that the mediator of the bisector $CU$ of the triangle $ABC$, the perpendicular to $AB$ at $U$, and the circumdiameter of $ABC$ passing through $C$ are concurrent. \\end{geothm}',' ', ' Example 219 ','2008/01/09')

INSERT INTO bibtheorem (teoId,bibrefId) VALUES ('GEO0094','chou88')

INSERT INTO figures (teoId,drawerId,code,dateSubmission,bibref,userId) VALUES ('GEO0094','3',' dim 110 100 point A 20 30 point B 90 30 point C 75 85 med mc A B med mb A C intersec O mc mb circle k O A bis s_c A C B line c A B intersec U s_c c line p C O med m C U intersec P p m drawdashline m drawcircle k cmark_lt P cmark_b U cmark_l O cmark_lb A cmark_rb B cmark_t C drawdashsegment P U drawsegment C O drawsegment C U drawsegment A B drawsegment A C drawsegment C B ','2008/01/09','chou88', 'gpreda1 ')
gclc figure0094.code figure0094.pic > figure0094.errors
Warning: fread() [function.fread]: Length parameter must be greater than 0 in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 328
Figura 744

    * Figure
    * figure0094.jpg
    * Description of the construction in natural language
    * figure0094.xml
    * Figure in SVG format
    * figure0094.svg

INSERT INTO demonstrations (teoId,proverId,code,dateSubmission,bibref,userId) VALUES ('GEO0094','2',' point A 20 30 point B 90 30 point C 75 85 med mc A B med mb A C intersec O mc mb circle k O A bis s_c A C B line c A B intersec U s_c c line p C O med m C U intersec P p m prove { perpendicular P U A B } ','2008/01/09', '','gpreda1 ')
The Proof's code 0094 is correct.

Processing the XML file, please wait
/usr/local/bin/gclc proof0094.code proofCode0094.xml -xml > proof0094.errors
Warning: fopen(proof0094.xml.bz2) [function.fopen]: failed to open stream: No such file or directory in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 508

Warning: filesize() [function.filesize]: stat failed for proof0094.xml.bz2 in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 509

Warning: fread(): supplied argument is not a valid stream resource in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 509

Warning: fclose(): supplied argument is not a valid stream resource in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 511

INSERT INTO theorems (teoId,userId,category,description,shortDescription,teoName,dateSubmission) VALUES ('GEO0095','gpreda1 ','Geometry','\\begin{geothm} Let $A_1$ and $B_1$ be midpoints of segments $AC$ and $BC$ in triangle $ABC$. Show that $A_1B_1$ is parallel to $AB$ and half of that segment. \\end{geothm}',' ', ' Triangle median line ','2008/01/09')

INSERT INTO bibtheorem (teoId,bibrefId) VALUES ('GEO0094','chou88')

INSERT INTO figures (teoId,drawerId,code,dateSubmission,bibref,userId) VALUES ('GEO0095','3',' dim 80 50 point A 20 10 point B 70 10 point C 35 40 drawsegment A B drawsegment A C drawsegment B C midpoint B_1 B C midpoint A_1 A C drawsegment A_1 B_1 midpoint M A B cmark_b M drawdashsegment A_1 M drawdashsegment B_1 M cmark_b A cmark_b B cmark_t C cmark_lt A_1 cmark_rt B_1 ','2008/01/09','', 'gpreda1 ')
gclc figure0095.code figure0095.pic > figure0095.errors
Warning: fread() [function.fread]: Length parameter must be greater than 0 in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 328
Figura 752

    * Figure
    * figure0095.jpg
    * Description of the construction in natural language
    * figure0095.xml
    * Figure in SVG format
    * figure0095.svg

INSERT INTO demonstrations (teoId,proverId,code,dateSubmission,bibref,userId) VALUES ('GEO0095','2',' point A 20 10 point B 70 10 point C 35 40 midpoint B_1 B C midpoint A_1 A C prove { parallel A_1 B_1 A B } ','2008/01/09', '','gpreda1 ')
The Proof's code 0095 is correct.

Processing the XML file, please wait
/usr/local/bin/gclc proof0095.code proofCode0095.xml -xml > proof0095.errors
Warning: fread() [function.fread]: Length parameter must be greater than 0 in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 497

INSERT INTO theorems (teoId,userId,category,description,shortDescription,teoName,dateSubmission) VALUES ('GEO0096','gpreda1 ','Geometry','\\begin{geothm} Cross ratio of four points $A$, $B$, $C$ and $D$ is same after central projection from point $O$ onto line $p$. \\end{geothm}',' ', ' Projection Keeps Cross Ratio ','2008/01/09')

INSERT INTO bibtheorem (teoId,bibrefId) VALUES ('GEO0094','chou88')

INSERT INTO figures (teoId,drawerId,code,dateSubmission,bibref,userId) VALUES ('GEO0096','3',' dim 130 85 point A 20 20 point C 40 20 point D 55 20 point B 90 20 point O 80 70 line ao A O line bo B O line co C O line do D O point A_1 32 30 point B_1 84 50 line ab1 A_1 B_1 intersec C_1 ab1 co intersec D_1 ab1 do cmark_b A cmark_b B cmark_b C cmark_b D cmark_r O cmark_rb A_1 cmark_rb C_1 cmark_rb D_1 cmark_rb B_1 drawsegment A B drawsegment A O drawsegment B O drawsegment C O drawsegment D O drawdashline ab1 ','2008/01/09','', 'gpreda1 ')
gclc figure0096.code figure0096.pic > figure0096.errors
Warning: fread() [function.fread]: Length parameter must be greater than 0 in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 328
Figura 760

    * Figure
    * figure0096.jpg
    * Description of the construction in natural language
    * figure0096.xml
    * Figure in SVG format
    * figure0096.svg

INSERT INTO demonstrations (teoId,proverId,code,dateSubmission,bibref,userId) VALUES ('GEO0096','2',' point A 20 20 point C 40 20 point D 55 20 point B 90 20 point O 80 70 line ao A O line bo B O line co C O line do D O online A_1 A O online B_1 B O line ab1 A_1 B_1 intersec C_1 ab1 co intersec D_1 ab1 do prove { equal { mult { sratio C A C B } { sratio D B D A } } { mult { sratio C_1 A_1 C_1 B_1 } { sratio D_1 B_1 D_1 A_1 } } } ','2008/01/09', '','gpreda1 ')
The Proof's code 0096 is correct.

Processing the XML file, please wait
/usr/local/bin/gclc proof0096.code proofCode0096.xml -xml > proof0096.errors
Warning: fread() [function.fread]: Length parameter must be greater than 0 in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 497

INSERT INTO theorems (teoId,userId,category,description,shortDescription,teoName,dateSubmission) VALUES ('GEO0097','gpreda1 ','Geometry','\\begin{geothm} Let $A$, $B$ and $C$ be three points on the line $p$, and let $A_1$, $B_1$ and $C_1$ be three points on the line $q$. Following intersections are created: $P = AB_1 \\cap A_1B$, $Q = AC_1 \\cap A_1C$ and $R = BC_1 \\cap B_1C$. Show that points $P$, $Q$ and $R$ are collinear. \\end{geothm}',' ', ' Pappus Hexagon Theorem ','2008/01/09')

INSERT INTO bibtheorem (teoId,bibrefId) VALUES ('GEO0094','chou88')

INSERT INTO figures (teoId,drawerId,code,dateSubmission,bibref,userId) VALUES ('GEO0097','3',' dim 110 90 point A 40 10 point B 90 10 point C 14.10 10 point A_1 35.20 38.20 point B_1 76.80 64.60 point C_1 48.30 46.39 line A_1B_1 A_1 B_1 line AB_1 A B_1 line AC_1 A C_1 line BA_1 B A_1 line BC_1 B C_1 line CA_1 C A_1 line CB_1 C B_1 intersec P AB_1 BA_1 intersec Q AC_1 CA_1 intersec S BC_1 CB_1 cmark_b A cmark_b B cmark_b C cmark_lt A_1 cmark_rb B_1 cmark_l C_1 cmark_rb P cmark_r Q cmark_r S drawdashline P S drawsegment A B_1 drawsegment A Q drawsegment B A_1 drawsegment B C_1 drawsegment C Q drawsegment C B_1 drawline A_1 C_1 drawline A C ','2008/01/09','', 'gpreda1 ')
gclc figure0097.code figure0097.pic > figure0097.errors
Warning: fread() [function.fread]: Length parameter must be greater than 0 in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 328
Figura 768

    * Figure
    * figure0097.jpg
    * Description of the construction in natural language
    * figure0097.xml
    * Figure in SVG format
    * figure0097.svg

INSERT INTO demonstrations (teoId,proverId,code,dateSubmission,bibref,userId) VALUES ('GEO0097','2',' point A 40 10 point B 90 10 online C A B point A_1 35.20 38.20 point B_1 76.80 64.60 online C_1 A_1 B_1 line A_1B_1 A_1 B_1 line AB_1 A B_1 line AC_1 A C_1 line BA_1 B A_1 line BC_1 B C_1 line CA_1 C A_1 line CB_1 C B_1 intersec P AB_1 BA_1 intersec Q AC_1 CA_1 intersec S BC_1 CB_1 prove { collinear P Q S } ','2008/01/09', '','gpreda1 ')
The Proof's code 0097 is correct.

Processing the XML file, please wait
/usr/local/bin/gclc proof0097.code proofCode0097.xml -xml > proof0097.errors
Warning: fread() [function.fread]: Length parameter must be greater than 0 in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 497

INSERT INTO theorems (teoId,userId,category,description,shortDescription,teoName,dateSubmission) VALUES ('GEO0098','gpreda1 ','Geometry','\\begin{geothm} Show that in any triangle, the orthocenter, the centroid and the center of circumscribed circle are collinear. \\end{geothm}',' ', ' Eualer Line Theorem ','2008/01/09')

INSERT INTO bibtheorem (teoId,bibrefId) VALUES ('GEO0094','chou88')

INSERT INTO figures (teoId,drawerId,code,dateSubmission,bibref,userId) VALUES ('GEO0098','3',' dim 110 110 point A 20 20 point B 90 20 point C 70 80 midpoint C_1 A B midpoint A_1 B C line at A A_1 line ct C C_1 intersec T at ct med a B C med c A B intersec O a c line ab A B line bc B C foot C_2 C ab foot A_2 A bc line ah A A_2 line ch C C_2 intersec H ah ch line oth O T drawline oth drawdashsegment A A_2 drawdashsegment C C_2 drawdashsegment O A_1 drawdashsegment O C_1 drawdashsegment A A_1 drawdashsegment C C_1 cmark_rb H cmark_t O cmark_rb T cmark_b A cmark_b B cmark_t C cmark_b C_1 cmark_b C_2 cmark_rt A_1 cmark_rt A_2 drawsegment A B drawsegment A C drawsegment C B ','2008/01/09','', 'gpreda1 ')
gclc figure0098.code figure0098.pic > figure0098.errors
Warning: fread() [function.fread]: Length parameter must be greater than 0 in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 328
Figura 776

    * Figure
    * figure0098.jpg
    * Description of the construction in natural language
    * figure0098.xml
    * Figure in SVG format
    * figure0098.svg

INSERT INTO demonstrations (teoId,proverId,code,dateSubmission,bibref,userId) VALUES ('GEO0098','2',' point A 20 20 point B 90 20 point C 70 80 midpoint C_1 A B midpoint A_1 B C line at A A_1 line ct C C_1 intersec T at ct med a B C med c A B intersec O a c line ab A B line bc B C foot C_2 C ab foot A_2 A bc line ah A A_2 line ch C C_2 intersec H ah ch line oth O T prove { equal { sratio H T T O } { 2 } } ','2008/01/09', '','gpreda1 ')
The Proof's code 0098 is correct.

Processing the XML file, please wait
/usr/local/bin/gclc proof0098.code proofCode0098.xml -xml > proof0098.errors
Warning: fread() [function.fread]: Length parameter must be greater than 0 in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 497

INSERT INTO theorems (teoId,userId,category,description,shortDescription,teoName,dateSubmission) VALUES ('GEO0099','gpreda1 ','Geometry','\\begin{geothm} Prove that in any triangle midpoints of each side, feet of each altitude and midpoints of the segments of each altitude from its vertex to the orthocenter lie on circle. \\end{geothm}',' ', ' Nine Points Circle ','2008/01/09')

INSERT INTO bibtheorem (teoId,bibrefId) VALUES ('GEO0094','chou88')

INSERT INTO figures (teoId,drawerId,code,dateSubmission,bibref,userId) VALUES ('GEO0099','3',' dim 110 110 point A 20 20 point B 90 20 point C 80 100 line ab A B line ac A C line bc B C foot D A bc foot E B ac foot F C ab midpoint G A B midpoint J B C midpoint I C A line ad A D line be B E intersec H ad be midpoint K A H midpoint L B H midpoint M C H line kj K J line gm G M intersec O kj gm circle k O G drawcircle k drawdashline kj drawdashline gm cmark_b A cmark_b B cmark_t C cmark_r D cmark_l E cmark_b F cmark_b G cmark_lb H cmark_t I cmark_r J cmark_lb M cmark_b K cmark_t L cmark_t O drawsegment A B drawsegment A C drawsegment B C drawsegment A D drawsegment B E drawsegment C F ','2008/01/09','', 'gpreda1 ')
gclc figure0099.code figure0099.pic > figure0099.errors
Warning: fread() [function.fread]: Length parameter must be greater than 0 in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 328
Figura 784

    * Figure
    * figure0099.jpg
    * Description of the construction in natural language
    * figure0099.xml
    * Figure in SVG format
    * figure0099.svg

INSERT INTO demonstrations (teoId,proverId,code,dateSubmission,bibref,userId) VALUES ('GEO0099','2',' point A 20 20 point B 90 20 point C 80 100 line ab A B line ac A C line bc B C foot D A bc foot E B ac foot F C ab midpoint G A B midpoint J B C midpoint I C A line ad A D line be B E intersec H ad be midpoint K A H midpoint L B H midpoint M C H line kj K J line gm G M intersec O kj gm circle k O G prove { perpendicular G M G E } ','2008/01/09', '','gpreda1 ')
The Proof's code 0099 is correct.

Processing the XML file, please wait
/usr/local/bin/gclc proof0099.code proofCode0099.xml -xml > proof0099.errors
Warning: fread() [function.fread]: Length parameter must be greater than 0 in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 497

INSERT INTO theorems (teoId,userId,category,description,shortDescription,teoName,dateSubmission) VALUES ('GEO0100','gpreda1 ','Geometry','\\begin{geothm} Segment $AB$ is given. Let $m$ be median of $AB$ and let circle $k$ be circle with center $A$ and half-diameter $B$. If $C$ is the intersection of circle $k$ and median $m$, show that triangle $ABC$ is isosceles. \\end{geothm}',' ', ' The Construction of Isosceles Triangle ','2008/01/09')

INSERT INTO bibtheorem (teoId,bibrefId) VALUES ('GEO0094','chou88')

INSERT INTO figures (teoId,drawerId,code,dateSubmission,bibref,userId) VALUES ('GEO0100','3',' dim 110 110 point A 20 20 point B 90 20 med c A B circle k A B intersec2 C C_1 k c cmark_b A cmark_rb B cmark_rt C drawsegment A B drawsegment A C drawsegment C B drawline c drawcircle k ','2008/01/09','', 'gpreda1 ')
gclc figure0100.code figure0100.pic > figure0100.errors
Warning: fread() [function.fread]: Length parameter must be greater than 0 in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 328
Figura 792

    * Figure
    * figure0100.jpg
    * Description of the construction in natural language
    * figure0100.xml
    * Figure in SVG format
    * figure0100.svg

INSERT INTO demonstrations (teoId,proverId,code,dateSubmission,bibref,userId) VALUES ('GEO0100','2',' point A 20 20 point B 90 20 med c A B circle k A B intersec2 C C_1 k c prove { equal { mult { angle B A C } { angle B A C } } { 3 } } ','2008/01/09', '','gpreda1 ')
The Proof's code 0100 is correct.

Processing the XML file, please wait
/usr/local/bin/gclc proof0100.code proofCode0100.xml -xml > proof0100.errors
Warning: fopen(proof0100.xml.bz2) [function.fopen]: failed to open stream: No such file or directory in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 508

Warning: filesize() [function.filesize]: stat failed for proof0100.xml.bz2 in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 509

Warning: fread(): supplied argument is not a valid stream resource in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 509

Warning: fclose(): supplied argument is not a valid stream resource in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 511

INSERT INTO theorems (teoId,userId,category,description,shortDescription,teoName,dateSubmission) VALUES ('GEO0101',' ','Geometry','','', '','2008/01/09')

INSERT INTO bibtheorem (teoId,bibrefId) VALUES ('GEO0094','chou88')

INSERT INTO figures (teoId,drawerId,code,dateSubmission,bibref,userId) VALUES ('GEO0101','3','','2008/01/09','', ' ')
gclc figure0101.code figure0101.pic > figure0101.errors
Warning: fread() [function.fread]: Length parameter must be greater than 0 in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 328
Figura 800

    * Figure
    * figure0101.jpg
    * Description of the construction in natural language
    * figure0101.xml
    * Figure in SVG format
    * figure0101.svg

INSERT INTO demonstrations (teoId,proverId,code,dateSubmission,bibref,userId) VALUES ('GEO0101','2','','2008/01/09', '',' ')
The Proof's code 0101 is correct.

Processing the XML file, please wait
/usr/local/bin/gclc proof0101.code proofCode0101.xml -xml > proof0101.errors
Warning: fread() [function.fread]: Length parameter must be greater than 0 in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 497

Warning: fopen(proof0101.xml.bz2) [function.fopen]: failed to open stream: No such file or directory in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 508

Warning: filesize() [function.filesize]: stat failed for proof0101.xml.bz2 in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 509

Warning: fread(): supplied argument is not a valid stream resource in /home/pedro/public_html/PHP/ParserXML/parserGeoThms100Prbl.php on line 509

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25 Undefined variable. (Line: 6, position: 11) - mantem-se

44 Undefined variable. (Line: 9, position: 12)  - mantem-se

46 Warning: fread() - resolvido

50 Wrong variable type. (Line: 6, position: 13) - mantem-se

77 Warning: fread() - resolvido

78 Warning: fread() - resolvido

==========Provas=================

The Proof's code 0 is correct. - The conjecture successfully proved.

The Proof's code 1 is correct. - The conjecture successfully proved.

The Proof's code 2 is correct. - The conjecture successfully proved.

The Proof's code 3 is correct. - The conjecture not proved.

The Proof's code 4 is correct. - The conjecture successfully proved.

The Proof's code 5 is correct. - The conjecture not proved.

The Proof's code 6 is correct. - The conjecture successfully proved.

The Proof's code 7 is correct. - The conjecture not proved.          

The Proof's code 8 is correct.

The Proof's code 9 is correct.

The Proof's code 10 is correct.

There are errors in the proof's 11 code.
Syntax error: Unrecognized definition or command. (Line: 15, position: 69) 

The Proof's code 12 is correct.

The Proof's code 13 is correct.

The Proof's code 14 is correct.

The Proof's code 15 is correct.

The Proof's code 16 is correct.

The Proof's code 17 is correct.

The Proof's code 18 is correct.

The Proof's code 19 is correct.

The Proof's code 20 is correct.

The Proof's code 21 is correct.

The Proof's code 22 is correct.

The Proof's code 23 is correct.

There are errors in the proof's 24 code.
Syntax error: Unrecognized definition or command. (Line: 12, position: 111) 

The Proof's code 25 is correct.

The Proof's code 26 is correct.

The Proof's code 27 is correct.

The Proof's code 28 is correct.

The Proof's code 29 is correct.

The Proof's code 30 is correct.

The Proof's code 31 is correct.

The Proof's code 32 is correct.

The Proof's code 33 is correct.

The Proof's code 34 is correct.

The Proof's code 35 is correct.

The Proof's code 36 is correct.

The Proof's code 37 is correct.

The Proof's code 38 is correct.

The Proof's code 39 is correct.

The Proof's code 40 is correct.

The Proof's code 41 is correct.

The Proof's code 42 is correct.

The Proof's code 43 is correct.

The Proof's code 44 is correct.

The Proof's code 45 is correct.

The Proof's code 46 is correct.

The Proof's code 47 is correct.

The Proof's code 48 is correct.

The Proof's code 49 is correct.

There are errors in the proof's 50 code.
Syntax error: Wrong variable type. (Line: 6, position: 13)

The Proof's code 51 is correct.

The Proof's code 52 is correct.

The Proof's code 53 is correct.

The Proof's code 54 is correct.

The Proof's code 55 is correct.

The Proof's code 56 is correct.

The Proof's code 57 is correct.

The Proof's code 58 is correct.

The Proof's code 59 is correct.

The Proof's code 60 is correct.

The Proof's code 61 is correct.

The Proof's code 62 is correct.

The Proof's code 63 is correct.

The Proof's code 64 is correct.

The Proof's code 65 is correct.

The Proof's code 66 is correct.

The Proof's code 67 is correct.

The Proof's code 68 is correct.

The Proof's code 69 is correct.

The Proof's code 70 is correct.

The Proof's code 71 is correct.

The Proof's code 72 is correct.

The Proof's code 73 is correct.

The Proof's code 74 is correct.

The Proof's code 75 is correct.

The Proof's code 76 is correct.

The Proof's code 77 is correct.

The Proof's code 78 is correct.

The Proof's code 79 is correct.

The Proof's code 80 is correct.

The Proof's code 81 is correct.

The Proof's code 82 is correct.

The Proof's code 83 is correct.

The Proof's code 84 is correct.

The Proof's code 85 is correct.

The Proof's code 86 is correct.

The Proof's code 87 is correct.

The Proof's code 88 is correct.

The Proof's code 89 is correct.

The Proof's code 90 is correct.

The Proof's code 91 is correct.

The Proof's code 92 is correct.

The Proof's code 93 is correct.

The Proof's code 94 is correct.

The Proof's code 95 is correct.

The Proof's code 96 is correct.

The Proof's code 97 is correct.

The Proof's code 98 is correct.

The Proof's code 99 is correct.
