Exams › SSC CGL (Prelims) › General

If two circles of radii 6 cm and 2 cm have their centers 10 cm apart, what is the length of the direct common tangent?

1. 6 cm
2. 8 cm
3. 2 \sqrt{21} cm
4. \sqrt{37} cm

Correct answer: 2 \sqrt{21} cm

Solution

For a direct common tangent, the length between the points of contact is \(\sqrt{d^2-(r_1-r_2)^2}\). Here, \(d=10\), \(r_1=6\), and \(r_2=2\), so length = \(\sqrt{100-16}=\sqrt{84}=2\sqrt{21}\) cm.

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