Question 27
A circle $\omega$ is tangent to the side $BC$ of a triangle $ABC$ at point $T$. The side $AB$ intersects $\omega$ at points $P$ and $R$ ($A$ is closer to $P$ than $R$); the side $AC$ intersects $\omega$ at points $Q$ and $S$ ($A$ is closer to $Q$ than $S$). The lines $AT$, $BQ$ and $CP$ are concurrent. Prove that the lines $AT$, $BS$ and $CR$ are also concurrent.