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SSC CGL 2024 PYQ — Question 71

SSC CGL - 10 Sep 2024 - Shift 1 • Quantitative Aptitude • Q71

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Two circles of radii 18 cm and 12 cm touch each other externally. Find the length (in cm) of their direct common tangent.

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Correct answer: C

Explanation

The correct answer is option 3 i.e. 12612{\sqrt6}.

r1 = 18 cm, r2 = 12 cm,

d = r1 + r2 = 18 + 12 = 30 cm

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

Direct common tangent = 302−(18−12)2\sqrt{30^2 - (18 - 12)^2}

⇒ 900−36\sqrt{900 - 36}

⇒ 864\sqrt{864} = 12612\sqrt{6}