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CAT 2018 Slot 2 QA Question & Solution

GeometryEasy

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

Options

$5\sqrt{3}$
$2\pi$
$8$
$6\sqrt{2}$

Solution

Question Figure

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

Let us draw OM such that OM $\perp$ AB. 

In right angle triangle AMO,

$sin 30° = \dfrac{AM}{AO}$

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

Question Figure

In right angle triangle PNO,

$sin 60° = \dfrac{PN}{PO}$

$\Rightarrow$ PN = $\dfrac{\sqrt{3}}{2}$*PO = $\dfrac{5\sqrt{3}}{2}$

Therefore, PQ = 2*PN = $5\sqrt{3}$ cm