A chord of a circle of radius 12cm
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A chord of circle of radius 12cm subtends an angle of 120degree at the centre. Find the area of the corresponding segment of the circle.
Answered by admin @
Given:
Radius of circle = 12 cm
θ = 120°
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
Hence, the area of the corresponding segment of the circle is 88.44 cm².
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