Mathematics - Circle Question with Solution | TestHub

Let the circles $C_1:(x-\alpha {)}^2+(y-\beta {)}^2=r_1^2$ and $C_2:(x-8{)}^2+{\left(y-\frac{15}{2}\right)}^2=r_2^2$ touch each other externally at the point $(6,6)$. If the point $(6,6)$ divides the line segment joining the centres of the circles $C_1$ and $C_2$ internally in the ratio $2:1$, then $(\alpha +\beta )+4\left(r_1^2+r_2^2\right)$ equals