Question

a chord of a circle of radius 12 cm subtends on angle of 120 at the centre Find the area of the corresponding segment of the circle​

Answer 1

the area of the corresponding segment of the circle is 88.44 cm².

Given :-

Radius of circle = 12 cm

θ = 120°

to find :-

the area of the corresponding segment of the circle

solution :-

Area of the segment= {(π/360) × θ - sin θ/2 cos θ/2} r²

Area of the segment={(π) × 120/360 - sin 120/2 cos 120/2 } 12²

= {(π) × ⅓ - sin 60° cos 60° } ×144

= (π/3 - ½ × √3/2) × 144

= (π/3 × 144 - 144 × √3/4

= 48π - 36√3

= 12(4π - 3√3)

= 12( 4 × 3.14 - 3 × 1.73)

[π = 3.14 , √3= 1.73]

= 12 (12.56 - 5.19)

= 12 × 7.37

= 88.44 cm²

∴ the area of the corresponding segment of the circle is 88.44 cm².