AMC 12 2011a Problem 11

Circles $A, B,$ and $C$ each have radius 1. Circles $A$ and $B$ share one point of tangency. Circle $C$ has a point of tangency with the midpoint of $\overline{AB}.$ What is the area inside circle $C$ but outside circle $A$ and circle $B?$

\textbf{(A)}\ 3 - \frac{\pi}{2} \textbf{(B)}\ \frac{\pi}{2} \textbf{(C)}\ 2 \textbf{(D)}\ \frac{3\pi}{4} \textbf{(E)}\ 1+\frac{\pi}{2}