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# 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
2 months, 3 weeks ago