Q. 74.2( 307 Votes )

A chord of a circle of radius 12 cm subtends an angle of 120° at the centre. Find the area of the corresponding segment of the circle.
(Use π = 3.14 and √3 = 1.73)

Answer :

Let us draw a perpendicular OV on chord ST. It will bisect the chord ST and the angle O.

SV = VT

In ΔOVS,
As, 

= Cos 60o

=

OV = 6 cm

= Sin 60o

=

SV = 6√3 cm

ST = 2 × SV

= 2 × 6√3

= 12√3 cm

Area of ΔOST = × 12√3 × 6

= 36√3

= 36 × 1.73

= 62.28 cm2

Area of sector OSUT = × π × (12)2

=  × 3.14 × 144

= 150.72 cm2

Area of segment SUT = Area of sector OSUT - Area of ΔOST

= 150.72 - 62.28

= 88.44 cm2

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