Math, asked by ArijitSingh4341, 1 year ago

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

Answers

Answered by tanha7
3

Answer:

Step-by-step explanation:

Let r be the radius of a circle in which a cord. AB= 5cm subtends an angle of

60° at the center O. An another cord PQ which subtends an angle of 120° at

the center of the same circle. Draw perpendiculars OC on AB and OR on

PQ.

In right angled triangle BCO

BC/OB=sin30°

(5/2)cm/r. = 1/2. =>. r= 5 cm………….(1)

In right angled triangle QRO

QR/OQ=sin60°

(PQ/2)/r = √3/2

Putting r =5 from eqn.(1)

PQ/5=√3

PQ=5.√3 cms = 5×1.732. = 8.66 cms.

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