## Τετάρτη, 11 Οκτωβρίου 2017

### 2001 JBMO Shortlist 12 (GRE)

Consider the triangle ${ABC}$ with ${\angle A = 90^\circ}$ and ${\angle B \ne \angle C}$. A circle ${C(O,R) }$ passes through ${B}$ and ${C}$ and intersects the sides ${AB}$ and ${AC}$ at ${D}$ and ${E}$, respectively. Let ${S}$ be the foot of the perpendicular from ${A}$ to ${BC}$ and let ${K}$ be the intersection point of ${AS}$ with the segment ${DE}$. If ${M}$ is the midpoint of ${BC}$, prove that ${AKOM}$ is a parallelogram.

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