2009 Fermat Problem 25

In the diagram, three circles of radius 10 are tangent to each other and to a plane in three-dimensional space. Each of the circles is inclined at 45^\circ to the plane. There are three points where the circles touch each other. These three points lie on a circle parallel to the plane. The radius of this circle is closest to

\textbf{(A)}\ 6.9\quad \textbf{(B)}\ 7.1\quad \textbf{(C)}\ 7.3\quad \textbf{(D)}\ 7.5\quad \textbf{(E)}\ 7.7

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

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