Question 99
A circle $\omega$ is tangent to the sides of an angle $BAC$ at $B$ and $C$. A line $l$ intersects the segments $AB$ and $AC$ at $K$ and $L$, respectively. The circle $\omega$ meets $l$ at $P$ and $Q$. The points $S$ and $T$ are chosen on the segment $BC$ so that $KS \parallel AC$ and $LT \parallel AB$. Prove that the points $P$, $Q$, $S$, and $T$ are concyclic. (I. Bogdanov, P. Kozhevnikov)