MathDB
Equilateral triangle and midpoints

Source: JBMO Shortlist 2006

November 10, 2008
geometryparallelogramgeometry proposed

Problem Statement

Let ABC ABC be an equilateral triangle of center O O, and MāˆˆBC M\in BC. Let K,L K,L be projections of M M onto the sides AB AB and AC AC respectively. Prove that line OM OM passes through the midpoint of the segment KL KL.
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