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SSC CHSL 2024 PYQ — Question 63

SSC CHSL - 10 July 2024 - Shift 3 • Quantitative Aptitude • Q63

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The centres of two circles of radii 20 cm and 32 cm are 60 cm apart. What is the ratio of the length of the direct common tangent to the length of the transverse common tangent to these circles?

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Correct answer: A

Explanation

The correct answer is option 1 i.e. 33:73\sqrt3:\sqrt7 .

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

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

According to the given question,

Required ratio = 602−(32−20)2\sqrt{60^2 - (32 - 20)^2} : 602−(32+20)2\sqrt{60^2 - (32 + 20)^2}

⇒ 3600−144\sqrt{3600 - 144} : 3600−2704\sqrt{3600 - 2704}

⇒ 3456\sqrt{3456} : 896\sqrt{896}

⇒ 24624\sqrt{6} : 8148 \sqrt{14} = 33:73\sqrt3:\sqrt7