Question 4
Let $ABC$ be a triangle and $X$ an interior point. Lines $XA,XB,XC$ meet the circumcircle again at $P,Q,R$, respectively. Let $U$ lie on ray $XP$ (on line $XP$, with $P,U$ on the same side of $X$). The line through $U$ parallel to $AB$ meets $BQ$ at $V$; the line through $U$ parallel to $AC$ meets $CR$ at $W$. Prove that $Q,R,V,W$ lie on one circle.