AMC 12 2011a Problem 24

Consider all quadrilaterals $ABCD$ such that $AB=14$, $BC=9$, $CD=7$, and $DA=12$. What is the radius of the largest possible circle that fits inside or on the boundary of such a quadrilateral?

\textbf{(A)}\ \sqrt{15} \textbf{(B)}\ \sqrt{21} \textbf{(C)}\ 2\sqrt{6} \textbf{(D)}\ 5 \textbf{(E)}\ 2\sqrt{7}