Exams › SSC CGL (Prelims) › General

Two circles have radii 8 cm and 3 cm. The distance between their centers is 15 cm. What is the length of a direct common tangent?

1. 10 cm
2. 12 cm
3. 10√2 cm
4. 12√2 cm

Correct answer: 10√2 cm

Solution

For a direct common tangent, the length is $\sqrt{d^2-(r_1-r_2)^2}$. Here $d=15$, $r_1-r_2=5$, so the length is $\sqrt{15^2-5^2}=\sqrt{200}=10\sqrt{2}$ cm.

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