CAT 2018 Quant Questions

Question:
A chord of length 5 cm subtends an angle of 60° at the centre of a circle. The length, in cm, of a chord that subtends an angle of 120° at the centre of the same circle is

8
6√2
5√3
 \(2\pi \)
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Correct Answer: 3

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We are given that AB = 5 cm and \(\angle \) AOB = 60°

Let us draw OM such that OM \( \bot \) AB.

In right angle triangle AMO,

\(sin30{\rm{^\circ }} = \frac{{AM}}{{AO}}\)

\( \Rightarrow \) AO = 2*AM = 2*2.5 = 5 cm. Therefore, we can say that the radius of the circle = 5 cm.

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In right angle triangle PNO,

\(sin60{\rm{^\circ }} = \frac{{PN}}{{PO}}\)

\( \Rightarrow \) PN = \(\frac{{\sqrt 3 }}{2}\)*PO = \(\frac{{5\sqrt 3 }}{2}\)

Therefore, PQ = 2*PN = \(5\sqrt 3 \) cm

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CAT 2018 Quant Questions
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