Question 13
Let $ABCD$ be a convex quadrilateral. The diagonal $BD$ bisects the angle $\measuredangle CBA$. The circumcircle of triangle $ABC$ meets the segments $\overline{CD}$ and $\overline{DA}$ at the interior points $P$ and $Q$ respectively. The parallel to the line $AC$ through the point $D$ meets the lines $BA$ and $BC$ at the points $R$ and $S$ respectively. Prove that the four points $P, Q, R$ and $S$ lie on a common circle.