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SSC CHSL 2024 PYQ — Question 57

SSC CHSL - 11 July 2024 - Shift 3 • Quantitative Aptitude • Q57

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Two circles of radii 3 units and r units, respectively, have a 6 units distance between their centers. If the length of the direct common tangent is 35\sqrt{35} units, then the value of r is ______ units.

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Correct answer: B

Explanation

The correct answer is option 2 i.e. 4.

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

35\sqrt{35} = 36−(3−r)2\sqrt{36-(3-r)^2}

⇒ 35 = 36 - 9 - r2 + 6r

⇒ r2 - 6r + 8 = 0

⇒ (r - 4)(r - 2) = 0

⇒ r = 2, 4

Sum of the radius should be more than the distance between the centres

So, r = 4 cm