Question 22
Let $\triangle ABC$ be an acute triangle with $|AC| \gt |AB|$. Let $N$ be the foot of the altitude from point $A$ to side $\overline{BC}$. Let $P$ be a point on the extension of $\overline{AB}$ over point $B$, and let $Q$ be a point on the extension of $\overline{AC}$ over point $C$ such that $BPQC$ is a cyclic quadrilateral. If $|NP| = |NQ|$, show that $N$ is the centre of the circle circumscribed to triangle $APQ$. (Japan)