2006 Fermat Problem 16

In the diagram, ABCD is a rectangle. If the area of the circle is equal to the area of the shaded region, the radius of the circle is

\textbf{(A)}\ \sqrt{\frac{6}{\pi}}\quad \textbf{(B)}\ \frac{6}{\pi}\quad \textbf{(C)}\ \frac{6}{\sqrt{\pi}}\quad \textbf{(D)}\ \sqrt{\frac{18}{\pi}}\quad \textbf{(E)}\ \frac{18}{\pi}

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