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A,B', C'; A',B, C'; A',B', C are collinear (IMO SL 1987-P12)

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August 19, 2010
geometrycircumcircleincentercollinearityIMO Shortlist

Problem Statement

Given a nonequilateral triangle ABCABC, the vertices listed counterclockwise, find the locus of the centroids of the equilateral triangles A′B′C′A'B'C' (the vertices listed counterclockwise) for which the triples of points A,B′,C′;A′,B,C′;A,B', C'; A',B, C'; and A′,B′,CA',B', C are collinear.
Proposed by Poland.
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