Question 39
Let $ABCD$ be a trapezoid with obtuse angle at vertex $D$. The diagonals $AC$ and $BD$ meet at $O$ and the line through $O$ parallel to $AB$ meets the circumcircle of $BCO$ again at $P$. The circumcircles of $ADO$ and $BCO$ intersect again at $Q$. Prove that the line $PQ$ bisects the segment $BC$.