MathNet 2014 Question 37

In quadrilateral $A B C D$, we have $A B=5$, $B C=6$, $C D=5$, $D A=4$, and $\angle A B C=90^{\circ}$. Let $A C$ and $B D$ meet at $E$. Compute $\frac{B E}{E D}$.



Supplemental illustration of the given configuration.