2004 Fermat Problem 16

A right-angled triangle has sides of length 6, 8 and 10. A circle is drawn so that the area inside the circle but outside this triangle equals the area inside the triangle but outside the circle. The radius of the circle is closest to

\textbf{(A)}\ 2.9\quad \textbf{(B)}\ 2.8\quad \textbf{(C)}\ 3.8\quad \textbf{(D)}\ 3.1\quad \textbf{(E)}\ 3.6

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

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