Question

Let C₁& C₂ are circles defined by x² + y² – 20x + 64 = 0 and x² + y² + 30x + 144 = 0. The length of shortest line segment PQ which is tangent to C₁ at P and C₂ at Q is

• A. 18
• B. 20
• C. 22
• D. None

Answer 1

Answer: (B)

20

Answer 2

Draw OM || PQ

Radius of C₁ = r₁ = 6

Radius of C₂ = r₂ = 9

Let OOў = d = 25

Now

d² = (r₁ + r₂)² + l²

\ l = $\sqrt{d^{2} - (r_{1} + r_{2})^{2}}$

Ю l = 20