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In the figure below, equilateral triangles ABC_{1} and A_{1}BC are drawn on the sides of a triangle ABC. If B_{1}, A_{2}, and C_{2} are the midpoints of AC, BC_{1}, and A_{1}B, respectively, prove that the triangle A_{2}B_{1}C_{2} is equilateral.

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Post or view a solution to the problem 1218 Last updated: May 26, 2016