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KLM is equilateral iff BAC = 60 degrees.

Source: Romanian IMO Team Selection Test TST 1999, problem 2

September 24, 2005
geometryincentergeometry proposed

Problem Statement

Let ABCABC be an acute triangle. The interior angle bisectors of ∠ABC\angle ABC and ∠ACB\angle ACB meet the opposite sides in LL and MM respectively. Prove that there is a point KK in the interior of the side BCBC such that the triangle KLMKLM is equilateral if and only if ∠BAC=60∘\angle BAC = 60^\circ.
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