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SSC CGL 2025 PYQ — Question 56

SSC CGL - 19 Sep 2025 - Shift 2 • Quantitative Aptitude • Q56

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Two circles, with radii of r1 and r2 respectively, have their centers separated by a distance of d. If the length of a direct common tangent is equal to the distance between the centers, which of the following is true?

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Correct answer: C

Explanation

The correct answer is option 3 i.e. r1 = r2.

Direct common tangent length =d2−(r1−r2)2=d= \sqrt{d^2 - (r_1 - r_2)^2}= d

⇒ d2−(r1−r2)2=d2d^2 - (r_1 - r_2)^2 = d^2

⇒ (r1−r2)2=0(r_1 - r_2)^2 = 0

⇒ r1 = r2