Exams › SSC CGL (Prelims) › General

Two circles of radii \(R_1\) and \(R_2\) have centers at a distance \(d\) apart. If the length of the transverse common tangent is 0, what can be said about \(d\)?

1. d = \(R_1 + R_2\)
2. d = \(R_1 - R_2\)
3. d < \(R_1 + R_2\)
4. Circles are concentric

Correct answer: d = \(R_1 + R_2\)

Solution

For two circles, the length of the transverse common tangent becomes zero when the circles touch externally. In that case, the distance between centers equals the sum of their radii, \(d=R_1+R_2\).

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