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SSC CGL 2024 PYQ — Question 71

SSC CGL - 23 Sep 2024 - Shift 1 • Quantitative Aptitude • Q71

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For two circles of radius 7 units and 72\frac{7}{2} units, whose centers are 15 units apart, what is the length of the direct common tangent in units? (Correct to 3 decimals places.)

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Correct answer: A

Explanation

The correct answer is Option 1 i.e. 14.586.

Direct common tangent(L) = d2−(R−r)2\sqrt{d^2-(R-r)^2}

here, R = Radius of larger circle, r = radius of smaller circle, and d = distance between the centers of the circles

⇒ L = 152−(7−3.5)2\sqrt{15^2-(7-3.5)^2}

⇒ L = 225−(3.5)2\sqrt{225-(3.5)^2}

⇒ L = 225−12.25\sqrt{225-12.25}

⇒ L = 212.75\sqrt{212.75}

⇒ L = 14.586