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AA", BB" and CC" are concurrent

Source: Donova Mathmatical Olympiad 2010

February 11, 2012
geometrygeometric transformationreflectionparallelogramhomothetyratiogeometry proposed

Problem Statement

Given a triangle ABCABC, let A′,B′,C′A',B',C' be the perpendicular feet dropped from the centroid GG of the triangle ABCABC onto the sides BC,CA,ABBC,CA,AB respectively. Reflect A′,B′,C′A',B',C' through GG to A′′,B′′,C′′A'',B'',C'' respectively. Prove that the lines AA′′,BB′′,CC′′AA'',BB'',CC'' are concurrent.
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