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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