Τετάρτη, 11 Οκτωβρίου 2017

2006 JBMO Shortlist 12

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

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