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Hexagon with twice the area of a triangle

Source: 2011 Czech & Slovak MO, District Round, Category A

August 13, 2011
geometrygeometric transformationreflectiongeometry unsolved

Problem Statement

Let ABCABC denote a triangle with area SS. Let UU be any point inside the triangle whose vertices are the midpoints of the sides of triangle ABCABC. Let A′A', B′B', C′C' denote the reflections of AA, BB, CC, respectively, about the point UU. Prove that hexagon AC′BA′CB′AC'BA'CB' has area 2S2S.
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