MathDB
A nice collinearity problem

Source: IMO Shortlist 2007, G8, AIMO 2008, TST 7, P2

July 13, 2008
geometryquadrilateralincircleTriangleIMO Shortlist

Problem Statement

Point P P lies on side AB AB of a convex quadrilateral ABCD ABCD. Let ω \omega be the incircle of triangle CPD CPD, and let I I be its incenter. Suppose that ω \omega is tangent to the incircles of triangles APD APD and BPC BPC at points K K and L L, respectively. Let lines AC AC and BD BD meet at E E, and let lines AK AK and BL BL meet at F F. Prove that points E E, I I, and F F are collinear. Author: Waldemar Pompe, Poland
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