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. please explain me in easy way?

Draw a perpendicular OV on chord ST. It will bisect the chord ST.

SV = VT

In ΔOVS,

Area of ΔOST

Now, Area of sector OSUT

∴Area of segment SUT = Area of sector OSUT - Area of  ΔOST=150.72-62.28

⇒Area of segment SUT = 88.44 

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Radius = r = 12 cm, Angle =  = 120°

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