Single correct option
Two circles of radii 9 cm and 4 cm touch each other externally. What is the length (in cm) of their direct common tangent?
- A. 10
- B. 12
- C. 13
- D. √65
Show answer and solution
Answer: (B) 12
Distance between centres = 9 + 4 = 13.
Direct common tangent length = √(d² − (r₁ − r₂)²) = √(169 − 25) = √144 = 12.
Shortcut: for externally touching circles this simplifies to 2√(r₁r₂) = 2√36 = 12.
13 is only the distance between the centres. For the direct tangent always subtract the square of the difference of the radii.
Direct common tangent length = √(d² − (r₁ − r₂)²) = √(169 − 25) = √144 = 12.
Shortcut: for externally touching circles this simplifies to 2√(r₁r₂) = 2√36 = 12.
13 is only the distance between the centres. For the direct tangent always subtract the square of the difference of the radii.
Saved on this device. Sign in or create a free account to keep it on every device.