2022 AIME II Problem 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 A B=2, O_{1} O_{2}=15, C D=16, and A B O_{1} C D O_{2} is a convex hexagon. Find the area of this hexagon.