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If A'B'C' is equilateral then so is ABC

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August 29, 2010
geometrycircumcircletrigonometrysymmetrygeometry unsolved

Problem Statement

Let M,N,PM,N,P be the midpoints of the sides BC,CA,ABBC, CA, AB of a triangle ABCABC. The lines AM,BN,CPAM, BN, CP intersect the circumcircle of ABCABC at points A′,B′,C′A',B', C', respectively. Show that if A′B′C′A'B'C' is an equilateral triangle, then so is ABC.ABC.
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