Two circles of radius 2.4 cm and 4 cm, respectively, have a common tangent. The distance between the centres of the two circles is 6.5 cm. If the common tangent does not intersect the line joining the centers, then find the length of a common tangent to the circles.
Show answer & explanation
Correct answer: D
Explanation
The correct answer is option 4 i.e. 6.3 cm.
O1D (r1) = 4 cm
O2E (r2) = 2.4 cm
Distance between the centers of the circles = O1O2 (d) = 6.5 cm
Common tangent (DE) = √[d2 - (r1 - r2)2]
= √[(6.5)2 - (4 - 2.4)2]
= √[42.25 - (1.6)2]
= √(42.25 - 2.56)
= √39.69
= 6.3 cm
Hence, the length of the common tangent is 6.3 cm.