Question 59
Let $ABCD$ be a cyclic quadrilateral inscribed in a circle $\gamma$. Let $X$ be a point on the extension of $AC$ such that $XB$ and $XD$ are tangent to $\gamma$. The tangent at $C$ intersects $XD$ at $Q$. Let $E$ be the intersection of $AQ$ with $\gamma$ distinct from $A$. Prove that lines $AD$, $BE$, and $CQ$ are concurrent.