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SSC CHSL 2024 PYQ — Question 64

SSC CHSL - 02 July 2024 - Shift 3 • Quantitative Aptitude • Q64

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Two circles of diameters 16 cm and 20 cm are such that the distance between their centers is 13 cm. What is the length (in cm) of a common tangent to these circles that does not intersect the line joining the centers?

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Correct answer: A

Explanation

The correct answer is option 1 i.e. 165\sqrt{165}.

The diameter of the first circle is 16 cm,

so its radius r1 = 16/2 = 8 cm

The diameter of the second circle is 20 cm,

so its radius r2 = 20/2 = 10 cm

The distance between the centers of the two circles is d = 13 cm

the length of the common external tangent:

⇒ L = 132−(10−8)2 \sqrt{13^2 - (10 - 8)^2}

⇒ L = 169−4 \sqrt{169 - 4}

⇒ L = 165 \sqrt{165}