2001 Fermat Problem 18

In the diagram, the two smaller circles have equal radii. Each of the three circles is tangent to the other two circles, and each is also tangent to sides of the rectangle. If the width of the rectangle is 4, then its length is

\textbf{(A)}\ 2+\sqrt{8}\quad \textbf{(B)}\ 3+\sqrt{8}\quad \textbf{(C)}\ 3+\sqrt{10}\quad \textbf{(D)}\ \sqrt{32}\quad \textbf{(E)}\ 4+\sqrt{3}

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