MathNet 2014 Question 18

Let $ABCD$ be a trapezoid with $AB \parallel CD$ and $\angle D = 90^{\circ}$. Suppose that there is a point $E$ on $CD$ such that $AE = BE$ and that triangles $AED$ and $CEB$ are similar, but not congruent. Given that $\frac{CD}{AB} = 2014$, find $\frac{BC}{AD}$.



Supplemental illustration; no additional hypothesis is imposed.