Exams › SSC CGL (Prelims) › General

Two circles of radii 9 cm and 4 cm touch each other externally. Find the length of their direct common tangent.

1. 13 cm
2. 12 cm
3. 10 cm
4. 11 cm

Correct answer: 12 cm

Solution

For two circles touching externally, the length of the direct common tangent is \(\sqrt{d^2-(r_1-r_2)^2}\), where \(d=r_1+r_2\). Here, \(d=13\) and \(r_1-r_2=5\), so the length is \(\sqrt{169-25}=12\) cm.

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