Question 61
Let $ABCD$ be quadrilateral inscribed in the circle $\omega$. Simedian of the angle $B$ of the triangle $\triangle ABD$ intersects $\omega$ at point $P$ and simedian of the angle $B$ of the triangle $\triangle CBD$ intersects $\omega$ at point $Q$. Prove that if $CP \cap AB = X$, $AQ \cap BC = Y$ then points $X$, $D$, $Y$ lie on a line.