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Triangle with A = 120

Source: Baltic Way 2000 Problem 4

February 13, 2009
geometryparallelogramgeometry unsolved

Problem Statement

Given a triangle ABC ABC with \angle A \equal{} 120^{\circ}. The points K K and L L lie on the sides AB AB and AC AC, respectively. Let BKP BKP and CLQ CLQ be equilateral triangles constructed outside the triangle ABC ABC. Prove that PQ \ge\frac{\sqrt 3}{2}\left(AB \plus{} AC\right).
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