Semicircle inscribed in a square

Geometry Level 4

Let ABCDABCD be a unit square. What is the area of the largest semicircle that can be inscribed inside it?

If your answer is of the form (abc)π(a-b\sqrt{c})\pi, where aa, bb and cc are integers and cc is square-free, write your answer as a+b+ca+b+c.

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