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Prove that this triangle is equilateral...

Source: My father

August 2, 2005
trigonometrysearchPrincetoncollege

Problem Statement

You have a triangle, ABCABC. Draw in the internal angle trisectors. Let the two trisectors closest to ABAB intersect at DD, the two trisectors closest to BCBC intersect at EE, and the two closest to ACAC at FF. Prove that DEFDEF is equilateral.
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