APMO 2010 - Asian Pacific Mathematics Olympiad Question 1

Let $ABC$ be a triangle with $\angle BAC\ne90^\circ$. Let $O$ be its circumcenter and $\Gamma$ the circumcircle of triangle $BOC$. Suppose that $\Gamma$ intersects segment $AB$ at $P\ne B$, and segment $AC$ at $Q\ne C$. Let $ON$ be a diameter of $\Gamma$. Prove that quadrilateral $APNQ$ is a parallelogram.

Newly drawn configuration: