2000 Fermat Problem 23

A circle is tangent to three sides of a rectangle having side lengths 2 and 4 as shown. A diagonal of the rectangle intersects the circle at points A and B. The length of AB is

\textbf{(A)}\ \sqrt{5}\quad \textbf{(B)}\ \frac{4\sqrt{5}}{5}\quad \textbf{(C)}\ \sqrt{5}-\frac{1}{5}\quad \textbf{(D)}\ \sqrt{5}-\frac{1}{6}\quad \textbf{(E)}\ \frac{5\sqrt{5}}{6}

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