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.

Note by Fidel Simanjuntak
1 year, 3 months ago

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  Easy Math Editor

MarkdownAppears as
*italics* or _italics_ italics
**bold** or __bold__ bold

- bulleted
- list

  • bulleted
  • list

1. numbered
2. list

  1. numbered
  2. list
Note: you must add a full line of space before and after lists for them to show up correctly
paragraph 1

paragraph 2

paragraph 1

paragraph 2

[example link](https://brilliant.org)example link
> This is a quote
This is a quote
    # I indented these lines
    # 4 spaces, and now they show
    # up as a code block.

    print "hello world"
# I indented these lines
# 4 spaces, and now they show
# up as a code block.

print "hello world"
MathAppears 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} \( \boxed{123} \)

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