circles 9th

MATHEMATICSMATHEMATICS

STANDARDSTANDARD: VI: VI

Bombay Cambridge GurukulBombay Cambridge Gurukul

Circle

S

Radius O

MCentre

M

Chord PQ

P

ED

Q

G Arc RE

O

F

Diameter DE

Circle in daily lifeCircle in musicCircle in sportsCircleCentreCircumferenceCircular regionRadiusDiameterChordArcSemicircleSegments of a circleCrossword

A circle

BACK

Many musical instruments have a circular surface. For example:

Bingo Drum Tabla

Snare Drum Bass DrumBACK

Five rings in the logo of Olympic gamesBACK

A circle

A circle can be drawn with the help of a circular object.For example: A circle drawn with the help of a coin.

A circle is a closed curve in a plane.

BACK

This fixed point (equidistant) inside a circle is called centre.

A circle is a closed curve consisting of all points in a plane which are at the same distance (equidistant) from a fixed point inside it.

OCentre

A circle

A circle has one and only one centre.

BACK

The distance around a circle is called its circumference.

O

CentreA circle

A

BACK

A circle divides a plane into three parts.

2. Interior of a circle

3. Exterior of a circle

A plane

OCentre

The interior of a circle together with its circumference is called the circular region.

1. The circle

BACK

Radius

A line segment that joins any point on the circle to its centre is called a radius.

MA point on the circle

CentreO

(Contd…)

Radii ( plural of radius) of a circle are equal in length.

Infinite number of radius can be drawn in a circle.

Radius

Centre

K

O

L

M

N

(Contd…)

BACK

Diameter AB

A line segment that joins any two points on the circle and passes through its centre is called a diameter.

A

B

A circleO Centre

(Contd…)

A circle

O

M

Infinite number of diameters can be drawn in a circle.

As the radii of a circle are equal in length, its diameters too are equal in length.

B

Q

(Contd…)

Centre

P

A

N

The length of the diameter of a circle is twice the length of its radius.

Radius OMCentre

MO

NRadius ON

Diameter MN

Diameter MN = Radius OM + Radius ON Radius OM = Radius ON

(Contd…)

BACK

A line segment that joins any two points on the circle is called a chord.

O

BA

A is a point on the circle

B is another point on the circle

A line segment that joins point A and B Chord

Diameter is also a chord of the circle.

OChord CD

C D

M

N

K

L

Chord MN

Chord KL

(Contd…)

Diameter CD

The diameter is the longest chord.

ODiameter CD

C D

M NChord MN

(Contd…)

C D

M N

Chord KL LK

LK

M NChord MN

O Centre

Infinite number of chords can be drawn in a circle.

Chord KL

Chord GH

G

H

BACK

OCentre

An arc is the distance between any two points on the circumference of a circle.

K L

(Contd…)

OCentre

LK

An arc is named by three points, of which two are the end points of the arc and the third one lies in between them.

XNaming an arc

(Contd…)

Arc KXL

OCentre

LK

X

Y

An arc divides the circle into two parts: the smaller arc is called the minor arc, the larger one is called the major arc.

Minor Arc KXL

Major Arc KYL

(Contd…)

An arc

An arc

BACK

Half of a circle is called a semicircle.

CentreO

DiameterD E

S

A semicircle is also an arc of the circle.

R

Arc DSE

Semicircle DRE

(Contd…)

Semicircle DSE

Arc DRE

ECentreO Diameter

Semicircle DSE

Semicircle DRE

Semicircular region

Semicircular region

The diameter of a circle divides it into 2 semicircular regions.

D

BACK

A chord divides the circular region into 2 parts, each of which is called a segment of the circle.

CentreO

D EChord DE

Minor segment of a circle

Major segment of a circle

S

R

(Contd…)

CentreO

D EChord DE

Minor segment of the circle

Major segment of the circle

P

Q

Minor arc DPE

Major arc DQE

The part of the circular region enclosed by a minor arc and the chord is called a minor segment. Minor segment does not contain the centre of the circle.

The part of the circular region enclosed by a major arc and the chord is called a major segment. Major segment contains the centre of the circle.

BACK

Radius Diameter Chord Arc SemiCircle

CentreO

Radius Diameter Chord Arc SemiCircle

Radius O

MCentre

M

O

Radius Diameter Chord Arc SemiCircle

Centre

EDDiameter DE

O

Radius Diameter Chord Arc SemiCircle

Centre

Chord PQ

P

Q

O

Radius Diameter Chord Arc SemiCircle

Centre

E

G

Arc PQR

O

F

Radius Diameter Chord Arc Semicircle

S

CentreO

Diameter

Semicircle

D E

Semicircle DSE

Semicircle

C2

C

UM

F

E

R

N

C

E

A

E

I

Down1. The distance between any two points on the circumference of the circle.2. The distance around the circle.

3. The distance from the centre of the circle to a point on the circle.

R

D

IU

S

R

1

C

3R

A

Across:4. The line segment that joins

any two points on the circle and passes through its centre.

5. A closed curve in a plane.6. All points on the circle are equidistant from this point.7. A line segment that joins any

two points on a circle.

4D A M TE E

5 I R L E

6C E N T E

H RO D7