Exams › SSC CGL (Prelims) › General

A common internal tangent connecting two circles is 12 cm long. The distance between the centers of the circles is 20 cm. If the larger circle has radius 11 cm, what is the radius of the smaller circle?

1. 3 cm
2. 4 cm
3. 5 cm
4. 6 cm

Correct answer: 5 cm

Solution

For a common internal tangent, the tangent length \(l\), center distance \(d\), and sum of radii satisfy \(l^2=d^2-(r_1+r_2)^2\). Substituting \(12^2=20^2-(11+r)^2\) gives \((11+r)^2=256\), so \(11+r=16\) and \(r=5\) cm.

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