2011 AMC 12A 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} \qquad \textbf{(B)}\ \sqrt{21} \qquad \textbf{(C)}\ 2\sqrt{6} \qquad \textbf{(D)}\ 5 \qquad \textbf{(E)}\ 2\sqrt{7}

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.