A powerpoint presentation about circle and its parts

1. MATHEMATICS
Geometry
Circle and
its
Parts

2. A circle

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

4. Five rings in the logo of Olympic games
A circle

5. 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.

6. A circle is a
closed curve
consisting of all
points
CentreO in a plane which
are at the same
distance
(equidistant) from
a fixed point
inside it.
This fixed point (equidistant) inside a circle is called
centre.
A circle has one and only one centre.

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

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

9. A
A circle
O Centre
B
A line segment that joins any two points on the circle and
passes through its centre is called a diameter.
(Contd…)

10. A circle
(Contd…)
P
Centre
A
Q
B
N
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.
C

11. Radius OM
Centre
M
O
N
Radius ON
Diameter MN
Radius OM = Radius ON
Diameter MN = Radius OM + Radius ON
The length of the diameter of a circle is twice the length of its
radius.
(Contd…)

12. A line segment that joins any two points on the circle is
called a chord.
O
A
A is a point on the
circle
B is another point
on the circle
B

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

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

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

16. K
C
KC
Secant KC
O
Centre
It is a line that intersects the circle at any two point
on the circle
line that contains a chord

17. K
C
KC
Secant KC
O
Centre
X
A
D
Infinite number of secants can be drawn in a circle.

18. K
C
O
Centre
D
It is a line that intersects the circle at exactly one
point on the circle. This point is called Point of
Tangency.
Point of
Tangency

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

20. 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
(Contd…)

21. L
X
Minor Arc KXL
K
O
Centre
Y
(Contd…)
An arc divides the circle into two parts: the smaller arc is
called the minor arc, the larger one is called the major arc.
Major Arc KYL

22. Measure of an Arc
Minor Arc: The measure is less than 180 degrees
Major Arc: The measure of the arc is
greater than 180 degrees

23. An arc

24. Half of a circle is called a semicircle.
O
Centre
Diameter
D E
S
A semicircle is also an arc of the circle
which measures exactly 180 degrees
R
(Contd…)
Semicircle DSE
Semicircle DSE

25. Central Angles
Central
Angle
(of a circle)
Central
Angle
(of a circle)
NOT A
Central
Angle
(of a circle)
• A central angle is an angle whose vertex is
the CENTER of the circle

26. An inscribed angle is an angle
whose vertex is on a circle and
whose sides contain chords.
Inscribed Angles
1 4
2
3
Is
NOT!
Is
NOT!
Is SO! Is SO!

27. Radius Diameter Chord Arc
Semi
Centre
O
Circle

28. Radius Diameter Chord Arc
Semi
M
O Centre
Circle

29. Radius Diameter Chord Arc
Semi
E
Circle
D
Diameter DE
O
Centre

30. Radius Diameter Chord Arc
Semi
Q
P
O
Centre
Circle

31. Radius Diameter Chord Arc
Semi
Centre
O
Circle

32. S
Diameter
Semicircle
D E
Sem
Semi
circle
Radius Diameter Chord Arc
O
Centre
Semicircle

33. M
O Centre
X
Secant Tangent

34. E
D
Diameter DE
O
Centre
T
Tangent
DT
Point of Tangency
Secant Tangent

35. TANGENT
CHORD
MINOR ARC
INSCRIBE ANGLE
DIAMETER

36. MAJOR ARC
CENTRAL ANGLE
SECANT
SEMICIRCLE
RADIUS

37. Angles in Circles

38. Central Angles
Central
Angle
(of a circle)
Central
Angle
(of a circle)
NOT A
Central
Angle
(of a circle)
• A central angle is an angle whose vertex is
the CENTER of the circle

39. CENTRAL ANGLES AND ARCS
The measure of a central
angle is equal to the measure
of the intercepted arc.

40. CENTRAL ANGLES AND ARCS
The measure of a central
angle is equal to the measure
of the intercepted arc.
Y
Z
O 110
Intercepted Arc
Central
Angle

41. EXAMPLE
Segment AD is a diameter. Find the values of x and y and z
in the figure.
x = 25°
y = 100°
z = 55°
A
B
O
C
D
55
x y
25
z

42. SUM OF CENTRAL ANGLES
The sum of the measures fo the central angles of a circle with
no interior points in common is 360º.
360º

44. 93o
117o
87o
65o
18o