The length of the direct common tangent is 24 cm for two circles whose radii are 16 cm and 6 cm. What is the distance between their centres?
Show answer & explanation
Correct answer: A
Explanation
The correct answer is option 1 i.e. 26 cm.
Direct common tangent (l) = √[d2 - (r1 - r2)2]
⇒ 24 = √[d2 - (16 - 6)2]
⇒ 24 = √(d2 - 100)
⇒ d2 - 100 = 576
⇒ d2 = 676
⇒ d = √676 = 26
Hence, the distance between the centers of the two circles is 26 cm.