Question 15
Two externally tangent circles $\omega_1$ and $\omega_2$ have centers $O_1$ and $O_2,$ respectively. A third circle $\Omega$ passing through $O_1$ and $O_2$ intersects $\omega_1$ at $B$ and $C$ and $\omega_2$ at $A$ and $D,$ as shown. Suppose that $AB = 2,$ $O_1O_2 = 15,$ $CD = 16,$ and $ABO_1CDO_2$ is a convex hexagon. Find the area of this hexagon.
