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)

In the mentioned figure, O is the centre of circle, AB is a chord AYB is the minor arc, OA=OB=Radius=12cm Arc AYB subtends an angle 120° at O. Area of Sector AOB = (120/360) × πr² = (1/3) × 3.14 × 12 × 12 cm² = 150.72 cm² By trigonometry, In △AOC AC = AO sin60° = 12 × √3/2 cm = 10.38 cm So, AB = 2AC = 2 × 10.38 cm = 20.76 cm And, OC = AO cos60° = 12 × 1/2 cm = 6 cm ∴Area of △AOB = 1/2 × AB × OC = 1/2 × 20.76 × 6 cm² = 62.28 cm² Area of the segment (Area of Shaded region) = Area of sector AOB - Area of △AOB = (150.72 - 62.28) cm² = 88.44 cm²