IR-MO-R2 2013 Problem 3

Let $M$ be the midpoint of (the smaller) arc $BC$ in circumcircle of triangle $ABC$ . Suppose that the altitude drawn from $A$ intersects the circle at $N$ . Draw two lines through circumcenter $O$ of $ABC$ paralell to $MB$ and $MC$ , which intersect $AB$ and $AC$ at $K$ and $L$ , respectively. Prove that $NK=NL$ .