TUYMAADA 2012 S6

Quadrilateral $ABCD$ is both cyclic and circumscribed. Its incircle touches its sides $AB$ and $CD$ at points $X$ and $Y$ , respectively. The perpendiculars to $AB$ and $CD$ drawn at $A$ and $D$ , respectively, meet at point $U$ ; those drawn at $X$ and $Y$ meet at point $V$ , and finally, those drawn at $B$ and $C$ meet at point $W$ . Prove that points $U$ , $V$ and $W$ are collinear.

Proposed by A. Golovanov