HMMT 2006 G7

Suppose $A B C D$ is an isosceles trapezoid in which $\overline{A B} \| \overline{C D}$. Two mutually externally tangent circles $\omega_{1}$ and $\omega_{2}$ are inscribed in $A B C D$ such that $\omega_{1}$ is tangent to $\overline{A B}, \overline{B C}$, and $\overline{C D}$ while $\omega_{2}$ is tangent to $\overline{A B}, \overline{D A}$, and $\overline{C D}$. Given that $A B=1, C D=6$, compute the radius of either circle.