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Let ABCDABCDABCD 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 (a−bc)π(a-b\sqrt{c})\pi(a−bc)π, where aaa, bbb and ccc are integers and ccc is square-free, write your answer as a+b+ca+b+ca+b+c.
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