The distance between the centres of two circles is 81 cm, and their radii are 42 cm and 51 cm. What is the length (in cm) of the direct common tangent to the circles?

Question

Question

This question was previously asked in

SSC CHSL Exam 2024 Tier-I Official Paper (Held On: 08 Jul, 2024 Shift 4)

Answer 1

Given:

Distance between the centers of two circles (d) = 81 cm

Radius of the first circle (r₁) = 42 cm

Radius of the second circle (r₂) = 51 cm

Formula used:

Length of the direct common tangent (L) is given by:

\(L = \sqrt{d^2 - (r₁ - r₂)^2}\)

Calculations:

Substitute the given values:

⇒ L = \( \sqrt{81^2 - (51 - 42)^2}\)

⇒ L = \( \sqrt{6561 - (9)^2}\)

⇒ L = \( \sqrt{6561 - 81}\)

⇒ L = \( \sqrt{6480}\)

⇒ L = \( \sqrt{6480} \, \text{cm}\)

⇒ L = 36√5 cm

∴ The length of the direct common tangent is 36√5.