If the radius of two circles be 6 cm and 9 cm and the length of the transverse common tangent be 20 cm, then find the distance between the two centres.
Show answer & explanation
Correct answer: A
Explanation
The correct answer is option 1 i.e. 25 cm.
Given that
If the radius of two circles be 6 cm and 9 cm,
R = 9 cm , r = 6 cm
the length of the transverse common tangent be 20 cm
Formula used
the length of the transverse common tangent = √[d2 − (R + r)2]
where, d = distance between the centers of circles
⇒ 20 = √[d2 − (R + r)2]
⇒ 400 = d2 − (9 + 6)2
⇒ d2 = 400 + 225 = 625
⇒ d = 25 cm