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SSC CHSL 2023 PYQ — Question 66

SSC CHSL - 07 Aug 2023 - Shift 1 • Quantitative Aptitude • Q66

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Find the distance (in cm) between the centres of two circles having radil of 32 cm and 24 cm, respectively, if the length of a direct common tangent to the two circles is given as 24724\sqrt{7} cm.

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Correct answer: C

Explanation

The correct answer is option 3 i.e. 64.

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

where d is distance between the centers of the circle and r1 and r2 are the radii of two circles.

According to the given question,

24724\sqrt{7} = d2−(32−24)2\sqrt{d^2 - (32 - 24)^2}

⇒ 576 × 7 = d2 - 64

⇒ d2 = 4032 + 64

⇒ d2 = 4096

⇒ d = 64