CEMC Cayley, 2001

Geometry Difficulty 3.0 AMC 10/12 Find the answer Canada

Square $ABCD$ with side length $2$ is inscribed in a circle, as shown. Using each side of the square as a diameter, semi-circular arcs are drawn. The area of the shaded region outside the circle and inside the semi-circles is

(A) $\pi$ (B) $4$ (C) $2\pi-2$ (D) $\pi+1$ (E) $2\pi-4$

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