Question 62
Inside a circle with centre $O$ and radius $r$, two points $A$ and $B$ symmetric with respect to $O$ are taken. A variable point $P$ on this circle is considered and the chord $P P^{\prime}$, perpendicular to $A P$, is drawn. Let $C$ be the point symmetric to $B$ with respect to $P P^{\prime}$. Find the locus of the point $Q$, the intersection of $P P^{\prime}$ with $A C$, as $P$ varies on the circle.