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:

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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Exercises

Areas Related to Circles - Exercise 12.1

Areas Related to Circles - Exercise 12.2

Areas Related to Circles - Exercise 12.3

Chapters

Real Numbers

Polynomials

Pair of Linear Equations in Two Variables

Quadratic Equations

Arithmetic Progressions

Triangles

Coordinate Geometry

Introduction to Trigonometry

Some Applications of Trigonometry

Circles

Areas Related to Circles

Surface Areas and Volumes

Statistics

Probability