Question 49
The quadrilateral $ABCD$ is inscribed in a circle which has diameter $BD$. Points $A'$ and $B'$ are symmetric to $A$ and $B$ with respect to the line $BD$ and $AC$ respectively. If the lines $A'C$, $BD$ intersect at $P$ and $AC$, $B'D$ intersect at $Q$, prove that $PQ$ is perpendicular to $AC$.