Question 107
Let $ABC$ be an acute triangle with $O$ the centre of its circumcircle. Point $Q$ lies on the circumcircle of $\triangle BOC$ such that $OQ$ is a diameter. Point $M$ lies on $CQ$ and point $N$ lies in the interior of segment $BC$ such that $ANCM$ is a parallelogram. Prove that the circumcircle of $\triangle BOC$ and the lines $AQ$ and $NM$ pass through one point.
