Question 33
Inscribed circle $\omega$ of a triangle $ABC$ touches its sides $AB$, $BC$, $CA$ at the points $K$, $L$, $M$ respectively. On the arc $KL$ of the circle $\omega$ that does not contain the point $M$ a point $S$ is chosen. Let $P$, $Q$, $R$, $T$ be the points of intersection of the lines $AS$ and $KM$, $ML$ and $SC$, $LP$ and $KQ$, $AQ$ and $PC$ respectively. If the points $R$, $S$ and $M$ are collinear, prove that $T$ also belongs to the line $SM$.