Three tangent circles of radii 2, 3 and 6
Problem
Circles $\Gamma_1$, $\Gamma_2$ and $\Gamma_3$ have radii $2$, $3$ and $6$. The circles $\Gamma_1$ and $\Gamma_2$ touch each other externally at $C$, and each touches $\Gamma_3$ internally: $\Gamma_1$ at $B$ and $\Gamma_2$ at $A$. Find the circumradius of triangle $ABC$.
The diagram
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