Mathematics Question from JEE Main 2024 · 8 April, Shift 1

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: