Question 159
Let $XYZT$ be a parallelogram and $A, B, C, D$ variable points on the sides $XY, XT, TZ, ZY$, respectively, such that $ABCD$ is a cyclic quadrilateral with circumcenter $O$, $AC \parallel XT$, and $BD \parallel XY$. Let $P$ be the intersection of lines $AD$ and $BC$, and $Q$ be the intersection of lines $AB$ and $CD$. Prove that the circle $(POQ)$ passes through a fixed point as $A, B, C, D$ vary according to the given restrictions.