circles 9th
TRANSCRIPT
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
