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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