# Semicircle inscribed in a square

Geometry Level 4

Let $$ABCD$$ 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 $$(a-b\sqrt{c})\pi$$, where $$a$$, $$b$$ and $$c$$ are integers and $$c$$ is square-free, write your answer as $$a+b+c$$.

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