Question 7
Let $ABCD$ be a convex parallelogram whose angle at $A$ is acute. Let $P$ and $Q$ be the reflections of $A$ in the lines $BC$ and $CD$, respectively. Moreover, the line $BD$ intersects the interiors of the segments $AP$ and $AQ$ at $R$ and $S$, respectively. Prove that the circumcircles of triangles $BRP$ and $DQS$ are tangent.