Question 160
In triangle $ABC$, the circle $\Gamma$ is tangent to the side $BC$ at $X$, and to the side $AC$ at $Y$. For an arbitrary point $P$ on the side $[AB]$, the second intersection of $XP$ with $\Gamma$ is $K$ and the second intersection of $YP$ with $\Gamma$ is $L$, the second intersection of $AK$ with $\Gamma$ is $R$ and the second intersection of $BL$ with $\Gamma$ is $S$. Show that the lines $XR$ and $YS$ intersect on $AB$.