## Τρίτη, 17 Οκτωβρίου 2017

### 2005 IMO Shortlist G6

The median $AM$ of a triangle $ABC$ intersects its incircle $\omega$ at $K$ and $L$. The lines through $K$ and $L$ parallel to BC intersect \omega again at $X$ and $Y$ .  The lines $AX$ and $AY$ intersect $BC$ at  $P$ and $Q$. Prove that $BP = CQ$.

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