Question

A chord of a circle of radius 12 subtends an angle of 120 ° at the centre . Find the area of the corresponding segment of circle.​

Answer 1

Given:-

• A chord of a circle of radius 12 cm subtends an angle of 120 ° at the centre.

To find:-

• The area of the corresponding segment of circle.

Solution:-

Here,

• Radius of circle = 12 cm
• θ = 120°

According to the question,

→ 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)

→ 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.

Answer 2

Answer:

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