IMAC 2014 Problem 2

A convex quadrilateral $ABCD$ is inscribed into a circle $\omega$ . Suppose that there is a point $X$ on the segment $AC$ such that the $XB$ and $XD$ tangents to the circle $\omega$ . Tangent of $\omega$ at $C$ , intersect $XD$ at $Q$ . Let $E$ ( $E\ne A$ ) be the intersection of the line $AQ$ with $\omega$ . Prove that $AD, BE$ , and $CQ$ are concurrent.