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The midpoints either are collinear or form equilateral trgle

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September 22, 2010
geometrycongruent trianglesmidpointscollinearIMO Shortlist

Problem Statement

Two congruent equilateral triangles ABCABC and A′B′C′A'B'C' in the plane are given. Show that the midpoints of the segments AA′,BB′,CC′AA',BB', CC' either are collinear or form an equilateral triangle.
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