Question

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 1

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

SV = VT

In ΔOVS,

Area of ΔOST = 1/2 x ST x VT

=1/2 x 12√3 x 6

= 36√3 = 36 x 1.73 = 62.28 cm²

Area of sector OSUT =

1/3 x 3.14 x 144 = 150.72 cm²

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

= 150.72 − 62.28

= 88.44 cm²