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SSC CGL 2024 PYQ — Question 60

SSC CGL - 23 Sep 2024 - Shift 3 • Quantitative Aptitude • Q60

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The length of the tangent drawn from a point 10 cm away from the centre of a circle with radius 4 cm is:

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Correct answer: C

Explanation

The correct answer is option 3 i.e. 221{2 \sqrt{21}}.

OP = 10 cm, OT = 4 cm (radius)

The tangent at any point of a circle is perpendicular to the radius through the point of contact.

So, ∠OTP = 90°

△OTP is a right-angled triangle.

So, OP2 = OT2 + PT2

⇒ 102 = 42 + PT2

⇒ 100 = 16 + PT2

⇒ PT2 = 100 - 16 = 84

⇒ PT = √84 = 2√21

Therefore, the length of the tangent drawn from the point is 2√21 cm.