Question 94
Let $ABCD$ be a convex trapezoid such that $\angle DAB = \angle ABC = 90^{\circ}$, $DA = 2$, $AB = 3$, and $BC = 8$. Let $\omega$ be a circle passing through $A$ and tangent to segment $\overline{CD}$ at point $T$. Suppose that the center of $\omega$ lies on line $BC$. Compute $CT$.