The distance between the centres of two circles of radii 2cm and 6 cm is 5 cm. Find the length of the direct common tangent.
Show answer & explanation
Correct answer: B
Explanation
The correct answer is option 2 i.e. 3 cm
Given that
The radius of a small circle (r) = 2 cm
The radius of a big circle (R) = 6 cm
The distance between circles (D) = 5 cm
Direct common tangent (DCT)2 = D2 - (R -r)2
Calculation
(DCT)2 = 52 - (6 - 2)2
⇒ (DCT)2 = 25 - 16
⇒ (DCT)2 = 9
⇒ DCT = 3 cm