MathDB
Collinear

Source: Iranian National Olympiad (3rd Round) 2002

October 5, 2006
geometryincentergeometry proposed

Problem Statement

II is incenter of triangle ABCABC. Incircle of ABCABC touches AB,ACAB,AC at X,YX,Y. XIXI intersects incircle at MM. Let CM∩AB=X′CM\cap AB=X'. LL is a point on the segment X′CX'C that X′L=CMX'L=CM. Prove that A,L,IA,L,I are collinear iff AB=ACAB=AC.
Back to ProblemsView on AoPS