2006 Fermat Problem 25

Three identical cones each have a radius of 50 and a height of 120. The cones are placed so that their circular bases are touching each other. A sphere is placed so that it rests in the space created by the three cones, as shown. If the top of the sphere is level with the tops of the cones, then the radius of the sphere is closest to

\textbf{(A)}\ 38.9\quad \textbf{(B)}\ 38.7\quad \textbf{(C)}\ 38.1\quad \textbf{(D)}\ 38.5\quad \textbf{(E)}\ 38.3

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

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