Question 14
Let $ABC$ be a triangle with circumcircle $\omega$ and circumcenter $O$. Denote by $M$ the midpoint of that arc $BC$ of $\omega$ which does not contain vertex $A$. Lines passing through $O$ parallel to $MB$ and $MC$ intersect sides $AB$ and $AC$ at points $K$ and $L$, respectively. If the perpendicular from vertex $A$ to side $BC$ intersects $\omega$ at point $N$, show that $NK = NL$.