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collinear points (maybe posted before)

Source: Austria 1985

July 7, 2009
geometrygeometric transformationreflectionprojective geometrygeometry unsolved

Problem Statement

A line meets the lines containing sides BC,CA,AB BC,CA,AB of a triangle ABC ABC at A1,B1,C1, A_1,B_1,C_1, respectively. Points A2,B2,C2 A_2,B_2,C_2 are symmetric to A1,B1,C1 A_1,B_1,C_1 with respect to the midpoints of BC,CA,AB, BC,CA,AB, respectively. Prove that A2,B2, A_2,B_2, and C2 C_2 are collinear.
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