# How big is the orange?

Geometry Level 3

A circle of radius x is inscribed in a square. What is the radius $$r$$ of the largest circle that can fit into one of the corners?

State the radius as $$r = x(a + b \sqrt{c})$$ where $$a, b, c,$$ are integers and $$c$$ is not divisible by the square of any prime. Find $$a+b+c$$.

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