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Convex quadrilateral

Source: Korea National Olympiad 2009 Problem 6

September 9, 2012
geometryincentergeometry proposed

Problem Statement

Let ABCABC be a triangle and P,Q(≠A,B,C) P, Q ( \ne A, B, C ) are the points lying on segments BC,CA BC , CA . Let I,J,K I, J, K be the incenters of triangle ABP,APQ,CPQ ABP, APQ, CPQ . Prove that PIJK PIJK is a convex quadrilateral.
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