MathNet 2013 Question 3

An isosceles trapezoid $ABCD$ with bases $AB$ and $CD$ has $AB = 13$, $CD = 17$, and height $3$. Let $E$ be the intersection of $AC$ and $BD$. Circles $\Omega$ and $\omega$ are circumscribed about triangles $ABE$ and $CDE$. Compute the sum of the radii of $\Omega$ and $\omega$.

Supplemental illustration (AI-generated):