Question 51
Points $A$, $C$, and $B$ lie on a line in that order such that $AC = 4$ and $BC = 2$. Circles $\omega_{1}$, $\omega_{2}$, and $\omega_{3}$ have $\overline{BC}$, $\overline{AC}$, and $\overline{AB}$ as diameters. Circle $\Gamma$ is externally tangent to $\omega_{1}$ and $\omega_{2}$ at $D$ and $E$ respectively, and is internally tangent to $\omega_{3}$. Compute the circumradius of triangle $CDE$.