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MATHEMATICS MATHEMATICS STANDARD STANDARD : VI : VI Circle

Circle ppt

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Page 1: Circle ppt

MATHEMATICSMATHEMATICS

STANDARDSTANDARD: VI: VI

CircleCircle

Page 2: Circle ppt

S

Radiu

s OM

Centre

M

Chord PQ

P

ED

Q

G Arc R

E

O

F

Diameter DE

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

Page 3: Circle ppt

A circle

BACK

Page 4: Circle ppt

Many musical instruments have a circular surface.

For example:

Bingo Drum Tabla

Snare Drum Bass DrumBACK

Page 5: Circle ppt

Five rings in the logo of Olympic gamesBACK

A circle

Page 6: Circle ppt

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

Page 7: Circle ppt

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.

Page 8: Circle ppt

The distance around a circle is called its circumference.

O

CentreA circle

A

Page 9: Circle ppt

A circle divides a plane into three parts.

2. Interior of a circle

3. Exterior of a circle

A plane

O

Centre

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

1. The circle

Page 10: Circle ppt

Radiu

s

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

MA point on the circle

CentreO

(Contd…)

Page 11: Circle ppt

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

Infinite number of radius can be drawn in a circle.

Radiu

s

Centre

K

O

L

M

N

(Contd…)

Page 12: Circle ppt

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…)

Page 13: Circle ppt

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

Page 14: Circle ppt

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

Radius OM

Centre

MO

NRadius ON

Diameter MN

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

(Contd…)

Page 15: Circle ppt

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

Page 16: Circle ppt

Diameter is also a chord of the circle.

O

Chord CDC D

M

N

K

L

Chord MN

Chord KL

(Contd…)

Diameter CD

Page 17: Circle ppt

The diameter is the longest chord.

O

Diameter CDC D

M NChord MN

(Contd…)

C D

M N

Chord KLLK

Page 18: Circle ppt

LK

M NChord MN

O Centre

Infinite number of chords can be drawn in a circle.

Chord KL

Chord GH

G

H

BACK

Page 19: Circle ppt

O

Centre

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

K L

(Contd…)

Page 20: Circle ppt

O

Centre

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

Page 21: Circle ppt

O

Centre

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…)

Page 22: Circle ppt

An arc

An arc

Page 23: Circle ppt

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

Page 24: Circle ppt

ECentre

O Diameter

Semicircle DSE

Semicircle DRE

Semicircular region

Semicircular region

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

D

BACK

Page 25: Circle ppt

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

Centre

O

D EChord DE

Minor segment of a circle

Major segment of a circle

S

R

(Contd…)

Page 26: Circle ppt

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

Page 27: Circle ppt

Radius Diameter Chord ArcSemiCircle

CentreO

Page 28: Circle ppt

Radius Diameter Chord ArcSemiCircle

Radiu

s OM

Centre

M

O

Page 29: Circle ppt

Radius Diameter Chord ArcSemiCircle

Centre

EDDiameter DE

O

Page 30: Circle ppt

Radius Diameter Chord ArcSemiCircle

Centre

Chord PQ

P

Q

O

Page 31: Circle ppt

Radius Diameter Chord ArcSemiCircle

Centre

E

G

Arc P

QRO

F

Page 32: Circle ppt

Radius Diameter Chord ArcSemicircle

S

CentreO

Diameter

Semicircle

D E

Semicircle DSE

Semicircle

Page 33: Circle ppt

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

Page 34: Circle ppt