MathNet 2017-part-06 — 176 problems (EN–VI) Question 31

In the cyclic quadrilateral $ABCD$, the sides $AB$, $DC$ meet at $Q$, the sides $AD$, $BC$ meet at $P$, $M$ is the midpoint of $BD$. If $\angle APQ = 90^\circ$, prove that $PM$ is perpendicular to $AB$.