1965 AHSME Problem 16

Let line AC be perpendicular to line CE. Connect A to D, the midpoint of CE, and connect E to B, the midpoint of AC. If AD and EB intersect in point F, and \overline{BC} = \overline{CD} = 15 inches, then the area of triangle DFE, in square inches, is:

\textbf{(A)}\ 50 \qquad \textbf{(B) }\ 50\sqrt {2} \qquad \textbf{(C) }\ 75 \qquad \textbf{(D) }\ \frac{15}{2}\sqrt{105}\qquad \textbf{(E) }\ 100

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