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SSC CGL 2023 PYQ — Question 72

SSC CGL - 27 July 2023 - Shift 2 • Quantitative Aptitude • Q72

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The distance between the centres of two circles having radii 22 cm and 18 cm, is 32 cm. The length (in cm) of the direct common tangent of the two circles is :

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Correct answer: A

Explanation

The correct answer is option 1 i.e. 2252 cm2\sqrt{252} \ \rm{cm}.

The length of the direct common tangent = L

the distance between the centres of the two circles = d = 32 cm

r1​ and r2 are the radii of the two circles

r1​ = 22 cm, r2 = 18 cm

r1​ − r2​ = 22 − 18 = 4cm

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

⇒ L = 322−(22−18​)2\sqrt{32^2 −(22 − 18​)^2}

⇒ L = 322−42\sqrt{32^2 − 4^2}

⇒ L = 1024−16\sqrt{1024 − 16}

⇒ L = 1008\sqrt{1008}

⇒ L = 2252 cm2\sqrt{252} \ \rm{cm}