1999 Cayley Problem 16

Three circles, each with a radius of 10\,\text{cm}, are drawn tangent to each other so that their centres are all in a straight line. These circles are inscribed in a rectangle which is inscribed in another circle. The area of the largest circle is

\textbf{(A)}\ 1000\pi\quad \textbf{(B)}\ 1700\pi\quad \textbf{(C)}\ 900\pi\quad \textbf{(D)}\ 1600\pi\quad \textbf{(E)}\ 1300\pi

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

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