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If DEF is equilateral then AD, BE and CR are concurrent

Source: Pan African Olympiad 2009

October 1, 2011
geometrygeometric transformationreflectiongeometry proposed

Problem Statement

Point PP lies inside a triangle ABCABC. Let D,ED,E and FF be reflections of the point PP in the lines BC,CABC,CA and ABAB, respectively. Prove that if the triangle DEFDEF is equilateral, then the lines AD,BEAD,BE and CFCF intersect in a common point.
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