1994 AHSME Problem 17

An 8 by 2\sqrt{2} rectangle has the same center as a circle of radius 2. The area of the region common to both the rectangle and the circle is

\textbf{(A)}\ 2\pi \qquad\textbf{(B)}\ 2\pi+2 \qquad\textbf{(C)}\ 4\pi-4 \qquad\textbf{(D)}\ 2\pi+4 \qquad\textbf{(E)}\ 4\pi-2

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.