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23/06/2021 12:00 pm
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A chord of a circle of radius 15 cm subtends an angle of 60° at the centre. Find the areas of the corresponding minor and major segments of the circle. (Use π = 3.14 and √3 = 1.73)
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23/06/2021 12:03 pm
Radius = 15 cm
θ = 60°
Area of sector OAPB = (60°/360°) × πr2 cm2
= 225/6 π cm2
Now, ΔAOB is equilateral as two sides are the radii of the circle and hence equal and one angle is 60°
Area of ΔAOB = (√3/4) × a2
= (√3/4) × 152
∴ Area of ΔAOB = 97.31 cm2
Now, area of minor segment APB = Area of OAPB – Area of ΔAOB
Area of minor segment APB = ((225/6)π – 97.31) cm2
= 20.43 cm2
Area of major segment = Area of circle – Area of segment APB
Or, area of major segment = (π×152) – 20.4
= 686.06 cm2