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SSC CHSL 2024 PYQ — Question 56

SSC CHSL - 10 July 2024 - Shift 2 • Quantitative Aptitude • Q56

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The length (in cm) of a direct common tangent to two circles of radii 14 cm and 5 cm whose centres are separated by a distance of 40 cm is:

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Correct answer: D

Explanation

The correct answer is Option 4 i.e. 1519\sqrt{1519}.

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

⇒ L = d2−(r1−r2)2\sqrt{d^2 - (r_1 - r_2)^2}

⇒ L = 402−(14−5)2\sqrt{40^2 - (14 - 5)^2}

⇒ L = 1600−92\sqrt{1600 - 9^2}

⇒ L = 1600−81\sqrt{1600 - 81}

⇒ L = 1519\sqrt{1519} cm