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Sample Question 20:
Convex quadrilateral \(ABCD\) has \(AB = 9\) and \(CD = 12\). Diagonals \(AC\) and \(BD\) intersect at \(E\), \(AC = 14\), and \(\triangle AED\) and \(\triangle BEC\) have equal areas. What is \(AE\)?
\(\textbf{(A)}\ \frac {9}{2}\qquad \textbf{(B)}\ \frac {50}{11}\qquad \textbf{(C)}\ \frac {21}{4}\qquad \textbf{(D)}\ \frac {17}{3}\qquad \textbf{(E)}\ 6\)