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ABC equilateral if MNP equilateral

Source: Romanian District Olympiad 2006, Grade 10, Problem 2

March 11, 2006
trigonometry

Problem Statement

Let ABCABC be a triangle and let M,N,PM,N,P be points on the sides BCBC, CACA and ABAB respectively such that APPB=BMMC=CNAN. \frac{AP}{PB} = \frac{BM}{MC} = \frac{CN}{AN}. Prove that triangle if MNPMNP is equilateral then triangle ABCABC is equilateral.
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