Question

Let C1 be the circle of radius 1 with the center at the origin. Let C2 be the circle of radius r with center at the point A = (4,1), where 1 < r < 3 . Two distinct common tangents PQ and ST of C1 and C2 are drawn. The tangent PQ touches C1 at P and C2 at Q. The tangent ST touches C1 at S and C2 at T. Midpoints of the line segments PQ and ST are joined to form a line that meets the x-axis at a point B. If AB = √5, then the value of r2 is :

Answer 1

The value of r2 is 2

Consider points M and N as the midpoints of line segments PQ and ST respectively. As a result, the line MN serves as the radical axis connecting two circles.
Equation of MN : 8x+2y-18+r2=0
on solving r2 is 2.
So, the correct answer is 2