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10.1Circles and Circumference
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
A circle
BACK
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
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
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
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
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 Centre
P
A
N
The length of the diameter of a circle is twice the length of its radius. d=2r and r=(1/2)·d
Radius OM Centre
M O
N Radius ON
Diameter MN
Diameter MN = Radius OM + Radius ON Radius OM = Radius ON
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
Diameter CD
The diameter is the longest chord.
O Diameter CD
C D
M N Chord MN
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
The distance around a circle is called its circumference. C=π·d or C=2·π·r
O
Centre A circle
A
BACK
O Centre
An arc is the distance between any two points on the circumference of a circle.
K L
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
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
An arc
An arc
BACK
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
Semicircle DSE
Arc DRE
Radius Diameter Chord Arc Semi Circle
Centre O
Radius Diameter Chord Arc Semi Circle
Centre
M
O
Radius Diameter Chord Arc Semi Circle
Centre
E D Diameter DE
O
Radius Diameter Chord Arc Semi Circle
Centre
P
Q
O
Radius Diameter Chord Arc Semi Circle
Centre
E
G
O
F
Radius Diameter Chord Arc 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
3 R
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.
4 D A M T E E
5 I R L E
6 C E N T E
H R O D 7
Circle Pairs Congruent Circles
G
H K
J
Circle Pairs
Tow Circles are Congruent Circles if and only if they have
congruent radii
Circle Pairs
B C
A
Concentric Circles
Circle Pairs
Concentric Circles are coplanar circles that have the same center
