Question 38
Point $D \notin \{B, C\}$ is chosen on segment $BC$ and point $A$ is chosen on the plane such that it does not lie on the line $BC$. Points $P$ and $Q$ are chosen such that $ABPD$ and $ACQD$ are parallelograms (with the vertices in this order). The circumcircles of triangles $BDP$ and $CDQ$ intersect in $R \neq D$. Prove that the points $P, Q, R$ are collinear.