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Prove that triangle ABC is equilateral

Source: Germany Bundeswettbewerb Mathematik 2001, Round 2, Problem 3

January 31, 2009
geometry unsolvedgeometry

Problem Statement

Let ABC ABC be a triangle. Points A′,B′,C′ A',B',C' are on the sides BC,CA,AB, BC, CA, AB, respectively such that we have \overline{A'B'} \equal{} \overline{B'C'} \equal{} \overline{C'A'} and \overline{AB'} \equal{} \overline{BC'} \equal{} \overline{CA'}. Prove that triangle ABC ABC is equilateral.
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