| | | GEO0001 -- Ceva's Theorem |
Theorem. [Ceva's Theorem] Let DeltaABC be a triangle and P be any point in the plane. Let D=AP cap CB, E=BP cap AC, and F=CP cap AB. Show that: (AF)/(FB) × (BD)/(DC) × (CE)/(EA) = 1 P should not be in the lines parallels to AC, AB and BC and passing through B, C and A respectively.
point A 60 10
point B 30 90
point C 80 90
point P 55 75
line a B C
line b A C
line c A B
line pa P A
line pb P B
line pc P C
intersec D a pa
intersec E b pb
intersec F c 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_lt F
cmark_rt E
cmark_t P
prove { equal { mult { mult { sratio A F F B } { sratio B D D C } } { sratio C E E A } } 1 }
| | | GEO0001 -- Ceva's Theorem |