Length of subtended chord

CAT 2018 Slot 2 · QA · Easy · Geometry

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A chord of length 5 cm subtends an angle of 60∘60^\circ at the centre of a circle. The length, in cm, of a chord that subtends an angle of 120∘120^\circ at the centre of the same circle is

  1. A.

    2π

  2. B.

    5√3

  3. C.

    6√2

  4. D.

    8

Answer

B

Explanation

A chord subtending 60∘60^\circ at the centre forms an equilateral triangle with the radii. Hence, radius r=5 cmr = 5\text{ cm}.

For a chord subtending 120∘120^\circ at the centre, its length LL is: L=2rsin⁡(120∘2)=2×5×sin⁡(60∘)=10×32=53 cmL = 2r \sin\left(\frac{120^\circ}{2}\right) = 2 \times 5 \times \sin(60^\circ) = 10 \times \frac{\sqrt{3}}{2} = 5\sqrt{3}\text{ cm}

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