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SSC CGL 2025 PYQ — Question 55

SSC CGL - 23 Sep 2025 - Shift 3 • Quantitative Aptitude • Q55

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

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Correct answer: C

Explanation

The correct answer is option 3 i.e. 102\sqrt{2} cm.

Radii = 8 cm and 3 cm

Distance between centers = 15 cm

Length of direct common tangent = d2−(R−r)2\sqrt{d^2 − (R − r)^2} = 152−(8−3)2\sqrt{15^2 − (8 − 3)^2} = 225−25\sqrt{225 − 25} = 200\sqrt{200} = 102\sqrt{2} cm