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Iranian tough nut: AA', BN, CM concur in Gergonne picture

Source: Iranian olympiad/round 3/2002

December 29, 2003
geometrysymmetrygeometric transformationincenterprojective geometrypoles and polars

Problem Statement

Let ABCABC be a triangle. The incircle of triangle ABCABC touches the side BCBC at A′A^{\prime}, and the line AA′AA^{\prime} meets the incircle again at a point PP. Let the lines CPCP and BPBP meet the incircle of triangle ABCABC again at NN and MM, respectively. Prove that the lines AA′AA^{\prime}, BNBN and CMCM are concurrent.
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