Question 80
Three circles $\Gamma, \Gamma_{1}, \Gamma_{2}$ with radii 6, 3, 2 respectively are given. $\Gamma_{1}$ and $\Gamma_{2}$ are externally tangent at $A$, while $\Gamma$ is internally tangent to both other circles, at $A_{1}$ and $A_{2}$ respectively. Determine the radius of the circle circumscribed about $A A_{1} A_{2}$.
(A) $2 \sqrt{6}$
(B) 5
(C) $\sqrt{2}+\sqrt{3}+\sqrt{6}$
(D) $4+\sqrt{3}$
(E) 6
(A) $2 \sqrt{6}$
(B) 5
(C) $\sqrt{2}+\sqrt{3}+\sqrt{6}$
(D) $4+\sqrt{3}$
(E) 6