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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

Question 3 Areas Related to Circles - Exercise 12.2

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:

NCERT Solutions - Mathematics , Class 10 chapter Areas Related to Circles Question 3 Solution image

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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