OMCC 2010 Problem 2

Let $ABC$ be a triangle and $L$ , $M$ , $N$ be the midpoints of $BC$ , $CA$ and $AB$ , respectively. The tangent to the circumcircle of $ABC$ at $A$ intersects $LM$ and $LN$ at $P$ and $Q$ , respectively. Show that $CP$ is parallel to $BQ$ .