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SSC CGL 2025 PYQ — Question 56

SSC CGL - 18 Sep 2025 - Shift 3 • Quantitative Aptitude • Q56

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Two circles have radii in the ratio 2: 1. The length of a direct common tangent is 8 cm, and the distance between their centers is 10 cm. What is the radius of the smaller circle?

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Correct answer: D

Explanation

The correct answer is Option 4 i.e. 6 cm.

Let the radii be R and r, with R : r = 2 : 1

Let R = 2r

Length of direct common tangent =d2−(R−r)2= \sqrt{d^2 - (R - r)^2} where d = Distance between centers = 10 cm

102−(2r−r)2=8\sqrt{10^2 - (2r - r)^2} = 8

⇒ 100−r2=8\sqrt{100 - r^2} = 8

⇒ 100 - r2 = 64

⇒ r2 = 100 - 64 = 36

⇒ r = 6 cm