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Romania TST 1993,problem 2,day 3

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August 14, 2009
geometry unsolvedgeometry

Problem Statement

Suppose that D,E,F D,E,F are points on sides BC,CA,AB BC,CA,AB of a triangle ABC ABC respectively such that BD\equal{}CE\equal{}AF and \angle BAD\equal{}\angle CBE\equal{}\angle ACF.Prove that the triangle ABC ABC is equilateral.
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