2002 Pascal Problem 24

In the diagram, ABC is a semi-circle with diameter AC, centre O and radius 1. Also, OB is perpendicular to AC. Using AB as a diameter, a second semi-circle AEB is drawn. The region inside this second semi-circle that lies outside the original semi-circle is shaded, as shown. The area of this shaded region is

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

If there are no answer choices shown, enter a numerical answer.

Full credit to this problem is given to the CEMC, you may view all Pascal contests here.