Online Geometry theorems, problems, solutions, and related topics.
See complete Problem 64Triangle, Incircle, Transversal. Level: High School, SAT Prep, College geometryPost your solutions or ideas in the comments.
By Menelaus's theorem, AG/GC*CE/EB*BD/DA = -1Remembering that CE=CF=e,DB=BE and FA=AD=d. we've (x+d+e)/x * e/EB *EB/d = 1. Hence, (x+d+e)/x * e/d = 1 or x = -e^2-ed/(e-d) = e(d+e)/(d-e) QED.Ajit: firstname.lastname@example.org