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Middle European Mathematical Olympiad 2012 - Team Compt. T-5

Source: Middle European Mathematical Olympiad 2012 - Team Compt. T-5

September 14, 2012
Asymptotegeometrycircumcircleperpendicular bisectorgeometry proposed

Problem Statement

Let K K be the midpoint of the side AB AB of a given triangle ABC ABC . Let L L and M M be points on the sides AC AC and BC BC, respectively, such that ∠CLK=∠KMC \angle CLK = \angle KMC . Prove that the perpendiculars to the sides AB,AC, AB, AC, and BC BC passing through K,L, K,L, and MM, respectively, are concurrent.
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