Question 112
From a point $A$ outside circle $\omega$, tangents $AS$ and $AT$ are drawn to the circle. Points $X$ and $Y$ are the midpoints of segments $AT$ and $AS$, respectively. Tangent $XR$ is drawn from point $X$ to the circle and $P$ and $Q$ are the midpoints of segments $XT$ and $XR$, respectively. If $XY$ and $PQ$ intersect each other at $K$, and $SX$ and $TK$ intersect at $L$, prove that $KRLQ$ is an inscribed quadrilateral.