Circles and Triangle

Given a circle (let's call it circle $O$ ) inscribed in a triangle $XYZ$ with $XY \neq XZ$ . The circle $O$ touches $YZ$ , $ZX$ , and $XY$ at $U$ , $V$ , and $W$ respectively. Point $R$ lies on $XZ$ and point $S$ lies on $XY$ , such that $RS$ and $YZ$ are parallel to each other. Let $P$ be a circle that passes through the point $R$ and $S$ , and $P$ touches the circle $O$ at $T$ . Is it true that $VW$ , $UT$ , and $RS$ intersect at one point?

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