CIRCLESMade by :- Amit choube

Class :- 10th ‘ B ’

Introduction

In this power point presentation we will discuss about• Circle and its related terms .• Concepts of perimeter and area of a circle .• Finding the areas of two special parts of a circular region

known as sector and segment . • Finding the areas of some combinations of plane figures

involving circles or their parts .

Contents

Circle and its related terms . Area of a circle .Areas related to circle . Perimeter of a circle . Sector of a circle and its area .

Segment of a circle and its

area Areas of combinations of plane

figures .

Circle – DefinitionThe collection of all the points in a plane which are at a fixed distance from in the plane is called a circle . orA circle is a locus of a point which moves in a plane in such a way that its distance from a fixed point always remains same.

1. Radius – The line segment joining the centre and any point on the circle is called a radius of the circle .

O P

Here , in fig. OP is radius of the circle with centre ‘O’ .

Related terms of circle

2. A circle divides the plane on which it lies into three parts . They are • The Interior of the circle . • The circle . Exterior • The exterior of the circle . Interior

circle Here , in the given fig . We can see that a circle divides the plane on which it lies into three parts .

3. Chord – if you take two points P and Q on a circle , then the line segment PQ is called a chord of the circle .4. Diameter – the chord which passes through the centre of the circle is called a diameter of the circle . O

P R Here in the given fig. OR is the diameter of the circle and PR is the chord of the circle . Note :- A diameter of a circle is the longest chord of the circle .

1. Arc – the piece of circle between two points is called an arc of the circle .

Q .

Major Arc PQR

P . . R Minor Arc PR

Here in the given fig. PQR is the major arc because it is the longer one whereas PR is the minor arc of the given circle . When P and Q are ends of a diameter , then both arcs are equal and each is called a semicircle

Segment – the region between a chord and either of its arc is called a segment of the circle .

Major segment

Minor segment

Here , in the given fig. We can clearly see major and minor segment .

Sector – the region between two radii , joining the centre to the end points of the arc is called a sector . A

B

Here in the given fig. you find that minor arc corresponds to minor sector and major arc correspondence to major sector .

Perimeter of a circle • The distanced covered by travelling around a circle is its

perimeter , usually called its circumference .

We know that circumference of a circle bears a constant ratio with its diameter .

(diameter = 2r)

Area of a circleArea of a circle is , where is the radius of the circle . We have verified it in class 7 , by cutting a circle into a number of sectors and rearranging them as shown in fig.

Area and circumference of semicircle Area of circle = Area of semi – circle = (Area of circle) Area of semicircle

and

Perimeter of circle = Perimeter of semi circle = Perimeter of semi circle =

Area of a sector .

Following are some important points to remember 1. A minor sector has an angle , (say) , subtended at

the centre of the circle , whereas a major sector has no angle .

2. The sum of arcs of major and minor sectors of a circle is equal to the circumference of the circle .

3. The sum of the areas of major and minor sectors of a circle is equal to the areas of the circle .

4. The boundary of a sector consists of an arc of the circle and the two radii .

If an arc subtends an angle of 180 at the centre , then its arc length is . If the arc subtends an angle of θ at the centre , then its arc length is If the arc subtends an angle θ , then the area of the corresponding sector is Thus the area A of a sector of angle θ then area of the corresponding sector is Now,

Area of a sector.

Area of a sector.

Some useful results to remember .1. Angle described by one minute hand in 60 minute =360 ͦ

Angle described by minute hand in one minute = Thus , minute hand rotates through an angle of 6 in one minute .

2. Angle described by hour hand in 12 hours = 360 ͦ

Angle described hour hand in one minute = Thus , hour hand rotates through 30 in one minute . ͦ

Area of a segment of a circle

Thank you