SarkariPYQ

SSC CGL 2023 PYQ — Question 64

SSC CGL - 25 July 2023 - Shift 1 • Quantitative Aptitude • Q64

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In the following figure, there are two circles that touch each other externally. The radius of the first circle with centre P is 25 cm. The radius of the second circle with centre Q is 4 cm. Find the length of their direct common tangent AB

Figure is not to scale and is only for representational purpose.

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Correct answer: C

Explanation

The correct answer is option 3 i.e. 20 cm.

According to the given question,

Distance between centres of the circles, PQ(d) = 25 + 4 = 29 cm

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

⇒ 292−(25−4)2\sqrt{29^2 - (25 - 4)^2}

⇒ 841−441\sqrt{841 - 441}

⇒ 400\sqrt{400} = 20 cm