Question 138
Let $ABCD$ be a rectangle and $E$ be a point on segment $AD$. We are given that quadrilateral $BCDE$ has an inscribed circle $\omega_{1}$ that is tangent to $BE$ at $T$. If the incircle $\omega_{2}$ of $ABE$ is also tangent to $BE$ at $T$, then find the ratio of the radius of $\omega_{1}$ to the radius of $\omega_{2}$.