# XYZ Triangle

Geometry Level pending

Given $$\triangle ABC$$ with circumcircle $$\Gamma$$, let $$X$$ be the midpoint of arc $$BAC$$ and let $$Y, Z$$ be the tangency points of the $$B, C$$ excircle with $$AC, AB$$, respectively. If $$XY = 7, YZ = 8$$ find $$[XYZ]$$. The answer can be expressed as $$p\sqrt{q}$$ where $$p,q$$ are positive integers and $$q$$ is square free. As your answer, submit $$p+q$$.

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