# To infinity and beyond

Geometry Level 4

If the radius of the largest circle which can be inscribed inside the region bounded by $$2y=16-x^2$$ and $$y=x$$ can be expressed in the form $$\sqrt{a-b\sqrt{c}}$$ where a and b are integers and $$c$$ is not divisible by the square of any prime, find $$a+b+c$$.

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