Mathematics

Problem

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(r_1^2 + r_2^2)

equals (a) 110 (b) 125 (c) 145 (d) 130