I really need a help! (2)

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 $T$. Prove that $VW$, $UT$, and $RS$ intersect at one point.

#Geometry

Easy Math Editor

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`2 \times 3`	$2 \times 3$
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Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$