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NCERT Solutions Class 10 Mathematics Solutions for Areas Related to Circles - Exercise 12.2 in Chapter 12 - Areas Related to Circles
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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 major segment of the circle. (Use π = 3.14 and √3 = 1.73)
Answer:
Given,
Radius = 15 cm
θ = 60°
So,
Area of sector OAPB = (60°/360°)×πr2 cm2
= 225/6 πcm2
Now, ΔAOB is equilateral as two sides are the radii of the circle and hence equal and one angle is 60°
So, Area of ΔAOB = (√3/4) ×a2
Or, (√3/4) ×152
∴ Area of ΔAOB = 97.31 cm2
Now, area of minor segment APB = Area of OAPB – Area of ΔAOB
Or, area of minor segment APB = ((225/6)π – 97.31) cm2 = 20.43 cm2
And,
Area of major segment = Area of circle – Area of segment APB
Or, area of major segment = (π×152) – 20.4 = 686.06 cm2
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