| | | GEO0006 -- Menelaus' Theorem |
Theorem. [Menelaus' Theorem] A transversal meets the three sides AB, BC, and CA of a triangle ABC in F, D, and E respectively. Then (AF)/(FB) = - (DC)/(BD) × (EA)/(CE). The non-degenerate condition is that A, B, and C are not on line EF.
dim 100 100
area 5 5 90 90
point A 30 20
point B 70 20
point C 40 70
point X 15 55
point Y 75 10
line a B C
line b A C
line c A B
line p X Y
intersec D a p
intersec E b p
intersec F c p
drawsegment A B
drawsegment A C
drawsegment B C
drawline p
cmark_b A
cmark_t B
cmark_t C
cmark_t D
cmark_lt E
cmark_rt F
prove { equal { signed_area3 D E F } { 0 } }
| | | GEO0006 -- Menelaus' Theorem |