Exams › SSC CGL (Prelims) › General

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

1. 6 cm
2. 10 cm
3. 12 cm
4. 13 cm

Correct answer: 12 cm

Solution

If two circles touch externally, the distance between their centers is 4 + 9 = 13 cm. The length of the direct common tangent is \(\sqrt{d^2-(r_1-r_2)^2}\) = \(\sqrt{13^2-5^2}\) = \(\sqrt{144}=12\) cm.

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