circles.ppt

MATHEMATICS
STANDARD: VI
Bombay Cambridge Gurukul
Bombay Cambridge Gurukul
Circle

S
Centre
M
P
E
D
Q
G
O
F
Diameter DE
Circle in daily life
Circle in music
Circle in sports
Circle
Centre
Circumference
Circular region
Radius
Diameter
Chord
Arc
Semicircle
Segments of a circle
Crossword

Many musical instruments have a circular surface.
For example:
Bingo Drum Tabla
Snare Drum Bass Drum
BACK

Five rings in the logo of Olympic games
BACK
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.
O
Centre
A circle
A circle has one and only
one centre.
BACK

The distance around a circle is called its circumference.
O
Centre
A circle
A
BACK

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
BACK

A line segment that joins any point on the circle to its centre
is called a radius.
M
A point on the circle
Centre
O
(Contd…)

 Radii ( plural of radius) of a circle are equal in length.
 Infinite number of radius can be drawn in a circle.
Centre
K
O
L
M
N
(Contd…)
BACK

A line segment that joins any two points on the circle and
passes through its centre is called a diameter.
A
B
A circle
O 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 OM
Centre
M
O
N
Radius 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
B
A
A is a point on the
circle
B is another point
on the circle

Diameter is also a chord of the circle.
O
Chord CD
C D
M
N
K
L
(Contd…)
Diameter CD

The diameter is the longest chord.
O
Diameter CD
C D
M N
Chord MN
(Contd…)
C D
M N
Chord KL
L
K

L
K
M N
Chord MN
O Centre
Infinite number of chords can be drawn in a circle.
G
H
BACK

O
Centre
An arc is the distance between any two points on the
circumference of a circle.
K L
(Contd…)

O
Centre
L
K
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.
X
Naming an arc
(Contd…)
Arc KXL

O
Centre
L
K
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…)

 Half of a circle is called a semicircle.
Centre
O
Diameter
D E
S
 A semicircle is also an arc of the circle.
R
Arc DSE
Semicircle DRE
(Contd…)
Semicircle DSE
Arc DRE

E
Centre
O 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.
Centre
O
D E
Chord DE
Minor segment of a circle
Major segment of a circle
S
R
(Contd…)

Centre
O
D E
Chord 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
Semi
Circle
Centre
O

Semi
Circle
Centre
M
O

Semi
Circle
Centre
E
D
Diameter DE
O

Semi
Circle
Centre
P
Q
O

Semi
Circle
Centre
E
G
O
F

Semi
circle
S
Centre
O
Diameter
Semicircle
D E
Semicircle DSE
Semicircle

C
2
C
U
M
F
E
R
N
C
E
A
E
I
Down
1. 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
I
U
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 T
E E
5 I R L E
6C E N T E
H R
O D
7

circles.ppt

circles.ppt

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