OSN 2019 Problem 6

Given a circle with center $O$ , such that $A$ is not on the circumcircle. Let $B$ be the reflection of $A$ with respect to $O$ . Now let $P$ be a point on the circumcircle. The line perpendicular to $AP$ through $P$ intersects the circle at $Q$ . Prove that $AP \times BQ$ remains constant as $P$ varies.