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SSC CHSL 2023 PYQ — Question 60

SSC CHSL 2023 - 03 Aug 2023 - Shift 4 • Quantitative Aptitude • Q60

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The distance between the centers of two circles having radii of 24 cm and 18 cm, respectively, is 48 cm. Find the length (in cm) of a direct common tangent to the two circles.

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Correct answer: B

Explanation

The correct answer is option 2 i.e. 18718\sqrt {7}.

The radius of the big circle R = 24 cm

The radius of the small circle r = 18 cm

Distance between the circle d = 48 cm

The length of a direct common tangent to two circles = d2−(R−r)2\sqrt{d^2-(R-r)^2}

= 482−(24−18)2\sqrt{48^2-(24-18)^2}

= 2304−36\sqrt{2304-36}

= 2268\sqrt{2268}

= 18718\sqrt {7}