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
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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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