Circle
-
Upload
ankithns102 -
Category
Documents
-
view
289 -
download
3
Transcript of Circle
![Page 1: Circle](https://reader033.fdocuments.in/reader033/viewer/2022061200/5472c7afb4af9f072b8b4709/html5/thumbnails/1.jpg)
MATHEMATICSMATHEMATICS
STANDARDSTANDARD: VI: VI
Bombay Cambridge GurukulBombay Cambridge Gurukul
Circle
![Page 2: Circle](https://reader033.fdocuments.in/reader033/viewer/2022061200/5472c7afb4af9f072b8b4709/html5/thumbnails/2.jpg)
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
![Page 3: Circle](https://reader033.fdocuments.in/reader033/viewer/2022061200/5472c7afb4af9f072b8b4709/html5/thumbnails/3.jpg)
A circle
BACK
![Page 4: Circle](https://reader033.fdocuments.in/reader033/viewer/2022061200/5472c7afb4af9f072b8b4709/html5/thumbnails/4.jpg)
Many musical instruments have a circular surface. For example:
Bingo Drum Tabla
Snare Drum Bass DrumBACK
![Page 5: Circle](https://reader033.fdocuments.in/reader033/viewer/2022061200/5472c7afb4af9f072b8b4709/html5/thumbnails/5.jpg)
Five rings in the logo of Olympic gamesBACK
A circle
![Page 6: Circle](https://reader033.fdocuments.in/reader033/viewer/2022061200/5472c7afb4af9f072b8b4709/html5/thumbnails/6.jpg)
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](https://reader033.fdocuments.in/reader033/viewer/2022061200/5472c7afb4af9f072b8b4709/html5/thumbnails/7.jpg)
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
![Page 8: Circle](https://reader033.fdocuments.in/reader033/viewer/2022061200/5472c7afb4af9f072b8b4709/html5/thumbnails/8.jpg)
The distance around a circle is called its circumference.
O
CentreA circle
A
BACK
![Page 9: Circle](https://reader033.fdocuments.in/reader033/viewer/2022061200/5472c7afb4af9f072b8b4709/html5/thumbnails/9.jpg)
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
![Page 10: Circle](https://reader033.fdocuments.in/reader033/viewer/2022061200/5472c7afb4af9f072b8b4709/html5/thumbnails/10.jpg)
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…)
![Page 11: Circle](https://reader033.fdocuments.in/reader033/viewer/2022061200/5472c7afb4af9f072b8b4709/html5/thumbnails/11.jpg)
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
![Page 12: Circle](https://reader033.fdocuments.in/reader033/viewer/2022061200/5472c7afb4af9f072b8b4709/html5/thumbnails/12.jpg)
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](https://reader033.fdocuments.in/reader033/viewer/2022061200/5472c7afb4af9f072b8b4709/html5/thumbnails/13.jpg)
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](https://reader033.fdocuments.in/reader033/viewer/2022061200/5472c7afb4af9f072b8b4709/html5/thumbnails/14.jpg)
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
![Page 15: Circle](https://reader033.fdocuments.in/reader033/viewer/2022061200/5472c7afb4af9f072b8b4709/html5/thumbnails/15.jpg)
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](https://reader033.fdocuments.in/reader033/viewer/2022061200/5472c7afb4af9f072b8b4709/html5/thumbnails/16.jpg)
Diameter is also a chord of the circle.
OChord CD
C D
M
N
K
L
Chord MN
Chord KL
(Contd…)
Diameter CD
![Page 17: Circle](https://reader033.fdocuments.in/reader033/viewer/2022061200/5472c7afb4af9f072b8b4709/html5/thumbnails/17.jpg)
The diameter is the longest chord.
ODiameter CD
C D
M NChord MN
(Contd…)
C D
M N
Chord KL LK
![Page 18: Circle](https://reader033.fdocuments.in/reader033/viewer/2022061200/5472c7afb4af9f072b8b4709/html5/thumbnails/18.jpg)
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](https://reader033.fdocuments.in/reader033/viewer/2022061200/5472c7afb4af9f072b8b4709/html5/thumbnails/19.jpg)
OCentre
An arc is the distance between any two points on the circumference of a circle.
K L
(Contd…)
![Page 20: Circle](https://reader033.fdocuments.in/reader033/viewer/2022061200/5472c7afb4af9f072b8b4709/html5/thumbnails/20.jpg)
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
![Page 21: Circle](https://reader033.fdocuments.in/reader033/viewer/2022061200/5472c7afb4af9f072b8b4709/html5/thumbnails/21.jpg)
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…)
![Page 22: Circle](https://reader033.fdocuments.in/reader033/viewer/2022061200/5472c7afb4af9f072b8b4709/html5/thumbnails/22.jpg)
An arc
An arc
BACK
![Page 23: Circle](https://reader033.fdocuments.in/reader033/viewer/2022061200/5472c7afb4af9f072b8b4709/html5/thumbnails/23.jpg)
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](https://reader033.fdocuments.in/reader033/viewer/2022061200/5472c7afb4af9f072b8b4709/html5/thumbnails/24.jpg)
ECentreO 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](https://reader033.fdocuments.in/reader033/viewer/2022061200/5472c7afb4af9f072b8b4709/html5/thumbnails/25.jpg)
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…)
![Page 26: Circle](https://reader033.fdocuments.in/reader033/viewer/2022061200/5472c7afb4af9f072b8b4709/html5/thumbnails/26.jpg)
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](https://reader033.fdocuments.in/reader033/viewer/2022061200/5472c7afb4af9f072b8b4709/html5/thumbnails/27.jpg)
Radius Diameter Chord Arc SemiCircle
CentreO
![Page 28: Circle](https://reader033.fdocuments.in/reader033/viewer/2022061200/5472c7afb4af9f072b8b4709/html5/thumbnails/28.jpg)
Radius Diameter Chord Arc SemiCircle
Radius O
MCentre
M
O
![Page 29: Circle](https://reader033.fdocuments.in/reader033/viewer/2022061200/5472c7afb4af9f072b8b4709/html5/thumbnails/29.jpg)
Radius Diameter Chord Arc SemiCircle
Centre
EDDiameter DE
O
![Page 30: Circle](https://reader033.fdocuments.in/reader033/viewer/2022061200/5472c7afb4af9f072b8b4709/html5/thumbnails/30.jpg)
Radius Diameter Chord Arc SemiCircle
Centre
Chord PQ
P
Q
O
![Page 31: Circle](https://reader033.fdocuments.in/reader033/viewer/2022061200/5472c7afb4af9f072b8b4709/html5/thumbnails/31.jpg)
Radius Diameter Chord Arc SemiCircle
Centre
E
G
Arc PQR
O
F
![Page 32: Circle](https://reader033.fdocuments.in/reader033/viewer/2022061200/5472c7afb4af9f072b8b4709/html5/thumbnails/32.jpg)
Radius Diameter Chord Arc Semicircle
S
CentreO
Diameter
Semicircle
D E
Semicircle DSE
Semicircle
![Page 33: Circle](https://reader033.fdocuments.in/reader033/viewer/2022061200/5472c7afb4af9f072b8b4709/html5/thumbnails/33.jpg)
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](https://reader033.fdocuments.in/reader033/viewer/2022061200/5472c7afb4af9f072b8b4709/html5/thumbnails/34.jpg)