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SSC CGL 2024 PYQ — Question 60

SSC CGL - 19 Sep 2024 - Shift 1 • Quantitative Aptitude • Q60

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AB is a chord of length 32 cm of a circle of radius 20 cm, the tangents at A and B intersect at a point T. Find length TA (rounded off to two digits after decimal).

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Correct answer: C

Explanation

The correct answer is option 3 i.e. 26.67 cm.

Here, AB = 32 cm and OA = OB = 20 cm

So, AM = BM = AB/2 = 32/2 = 16 cm

Also, OM=OA2−AM2=202−162OM=\sqrt{OA^2-AM^2}=\sqrt{20^2-16^2} = √(400 - 256) = √144 = 12 cm

In ΔAOM and ΔAOT,

∠AOM = ∠AOT and ∠AMO = ∠TAO = 90°

Then, ΔAOM and ΔAOT are similar.

OM/OA = AM/TA

⇒ 12/20 = 16/TA

⇒ 12 × TA = 20 × 16

⇒ 12 × TA = 320

⇒ TA = 320/12

⇒ TA = 80/3

⇒ TA = 26.666... cm = 26.67 (approx)

Therefore, the length of TA is 26.67 cm.