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SSC CGL 2024 PYQ — Question 59

SSC CGL - 09 Sep 2024 - Shift 1 • Quantitative Aptitude • Q59

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The distance between the centres of two circles of radii 22 cm and 10 cm is 37 cm. If the points of contact of a direct common tangent to these circles are M and Q, then find the length of the line segment MQ.

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Correct answer: A

Explanation

The correct answer is Option 1 i.e. 35 cm.

Given that, r1 = 10 cm

r2 = 22 cm

d = 37 cm

Length of direct common tangent = d2−(r2−r2)2\sqrt{d^2 - (r_2 - r_2)^2}

⇒ 372−(22−10)2\sqrt{37^2 - (22 - 10)^2}

⇒ 1369−144\sqrt{1369 - 144} 

⇒ 1225\sqrt{1225} = 35

Hence, the length of the direct common tangent of the circle is 35 cm.