Question

Let C₁ C₂ and be circles defined by (x - 10)² + y² = 36 and (x + 15)² + y² = 81 respectively. The length of the shortest line segment PQ that is tangent C₁ at P and to C₂ at Q is 

(a) 15 

(b) 18 

(c) 20 

(d) 24

Answer 1

Correct option is (c) 20

We have,

C₁ : (x - 10)² + y² = 36

C₂ : (x + 15)² + y² = 81

Centre of C₁ = ( 10, 0) and radius = 6 

Centre of C₂ = −( -15, 0) and radius = 9

The length of smallest line segment PQ is the indirect common tangent of circle