Problem 113

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Problem 113: (2009 AMC 10a, 23; 12a 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$

Solution

Exercise 113: Solution

Convex quadrilateral $ABCD$ has $AB=10$ and $CD=15$. Diagonals $AC$ and $BD$ intersect at $E$, $AC=20$, and $\triangle AED$ and $\triangle BEC$ have equal areas. What is $AE$?

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