# 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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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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