SarkariPYQ

SSC CHSL 2023 PYQ — Question 54

SSC CHSL - 08 Aug 2023 - Shift 1 • Quantitative Aptitude • Q54

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Two circles of radii 9 cm and 4 cm, respectively, touch each other externally at point A. PQ is the direct common tangent of those two circles of centres O and O', respectively. The length of PQ is equal to:

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Correct answer: D

Explanation

The correct answer is option 4 i.e. 12 cm.

Both circles touch externally, distance between the centres, OO' = (9 + 4) = 13 cm

Direct common tangent, PQ = d2−(r1−r2)2\sqrt{d^2 - (r_1 - r_2)^2}

⇒ PQ = 132−(9−4)2\sqrt{13^2 - (9 - 4)^2}

⇒ PQ = 169−25\sqrt{169 - 25}

⇒ PQ = 144\sqrt{144}

⇒ PQ = 12 cm