In a circle of radius 14 cm, an arc subtends an angle of 120° at the centre. If √3 = 1.73 then the area of the segment of the circle is

Radius of Circle = R = 14 cm

Angle Subtended by the arc = θ = 120°

Area of sector subtending 120° = = 22/7 × 14 × 14 × 120/360 cm^{2}

= 205.33 cm^{2}

In Triangle ABC

AC = BC = 14 cm = R

Area of triangle ABC = 1/2 × base × height

= 2 × 1/2 × R sin θ/2 × R × cos θ/2

= 2 × 1/2 × 14 × 14 × sin 60° × cos 60°

= 84.77 cm^{2}

Area of Segment = Area of sector subtending 120° - Area of triangle ABC

= 205.33 – 84.77 cm^{2} = 120.56 cm^{2}

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