MathNet 2010 — Part 07 Question 94

Let $ABCD$ be an isosceles trapezoid such that $AB = 10$, $BC = 15$, $CD = 28$, and $DA = 15$. There is a point $E$ such that $\triangle AED$ and $\triangle AEB$ have the same area and such that $EC$ is minimal. Find $EC$.