# Find area of triangle

Geometry Level 5

Triangle $$ABC$$ has an inradius of $$5$$ and a circumradius of $$16$$.

If $$2\cos B = \cos A + \cos C$$, then the area of triangle $$ABC$$ can be expressed as $$\dfrac{x\sqrt{y}}{z}$$, where $$x, y$$ and $$z$$ are positive integers such that $$x$$ and $$z$$ are relatively prime and $$y$$ is not divisible by the square of any prime.

Find $$x+y+z$$.

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