TR-MO 2021 Problem 3

A circle $\Gamma$ is tangent to the side $BC$ of a triangle $ABC$ at $X$ and tangent to the side $AC$ at $Y$ . A point $P$ is taken on the side $AB$ . Let $XP$ and $YP$ intersect $\Gamma$ at $K$ and $L$ for the second time, $AK$ and $BL$ intersect $\Gamma$ at $R$ and $S$ for the second time. Prove that $XR$ and $YS$ intersect on $AB$ .