Question

If A is a point on the circle x2 + y2 = 1 and B is a point on the circle x2 + y2 - 10x + 21 = 0, then the minimum value of AB is

(A) 1

(B) 2

(C) 4

(D) 8

Answer 1

Correct option (b) 2

Explanation :

Suppose the centres of the two circles are O(0, 0) and C(5, 0) (Fig.). The radii of the circles are 1 and 2. Suppose the line OC meets the circles at points P and Q, respectively, so that P = (1, 0) and Q = (3, 0). Minimum value of AB occurs when A = P and B = Q. Therefore, the minimum value of AB = 5 - (1 + 2) = 2.