CAYLEY 2001 Problem 20

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

Image

Answer Choices
A. \pi
B. 4
C. 2\pi-2
D. \pi+1
E. 2\pi-4