This document is a lesson on circles taught by Mr. Airil Ahmad. It defines key terms related to circles like circumference, diameter, radius, chord, and arc. It explains properties of chords, including that a radius perpendicular to a chord bisects it and that equal chords are equidistant from the center. It also covers properties of circles, such as angles subtended at the circumference by the same arc being equal. The document provides examples of using circle properties to solve problems involving finding missing lengths.

1. Friday, January 25, 2013
AIRIL AHMAD

2. Friday, January 25, 2013
CIRCLES
BY
MR.AIRIL AHMAD
AIRIL AHMAD

3. Friday, January 25, 2013
CIRCLE
CIRCUMFERENCE MINOR SECTOR
DIAMETER ARC
RADIUS MINOR ARC
AREA OF SECTOR MAJOR ARC
MAJOR SECTOR CHORD
AIRIL BIN AHMAD

4. Friday, January 25, 2013
Where can you find the arc around you?
AIRIL BIN AHMAD

5. Friday, January 25, 2013
CHORD AND ARC
1. A chord is a straight line that joins
any two points on the circumference
of a circle.
2. An arc is a curved line that joins
any two points on the circumference
of a circle.
AIRIL BIN AHMAD

6. Friday, January 25, 2013
CHORD AND ARC
CHORD
ARC
AIRIL BIN AHMAD

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PROPERTIES OF CHORD
1. A radius that is
perpendicular to a chord
divides the chord into two
equal parts.
AIRIL BIN AHMAD

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PROPERTIES OF CHORD
5cm X cm
AIRIL BIN AHMAD

9. Friday, January 25, 2013
PROPERTIES OF CHORD
2. Equal chords in a circle are
equidistant from the centre.
AIRIL BIN AHMAD

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PROPERTIES OF CHORD
14 c
m
14 cm
AIRIL BIN AHMAD

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PROPERTIES OF CHORD
3. Two chords of the same
length cut arcs of the same
length.
AIRIL BIN AHMAD

12. Friday, January 25, 2013
PROPERTIES OF CHORD
14 c
m
14 cm
AIRIL BIN AHMAD

13. Friday, January 25, 2013
PYTHAGORAS’ THEOREM
x = 3 +4
2 2
3cm x cm x = 9 + 16
4cm
x = 25
x =5 AIRIL BIN AHMAD

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Trigonometry
3 4 5 8 15 17
5 12 13 9 12 15
6 8 10 10 24 26
7 24 25 12 16 20
AIRIL BIN AHMAD

15. Friday, January 25, 2013
Example 1:
P
From the figure find:
a. AQ= …………cm
b. OA= …………cm
O c. OR= …………cm
3 cm d. OP= …………cm
Q
A
4 cm
B e. QR= …………cm
R AIRIL BIN AHMAD

16. Friday, January 25, 2013
Example 2: Given that AB=16cm and
OQ=6cm from the
P
figure find:
a. AQ= …………cm
S
b. OS= …………cm
c. OP= …………cm
O
d. OA= …………cm
6 cm
Q e. OR= …………cm
A B
f. QR= …………cm
R AIRIL BIN AHMAD

17. Friday, January 25, 2013
Example 3: Given that AB=30cm and
OC=8cm from the
D
figure find:
a. AC= …………cm
b. CB= …………cm
c. OA= …………cm
O
d. OD= …………cm
8 cm
e. OB= …………cm
A B f. DC= …………cm
C
AIRIL BIN AHMAD

18. Friday, January 25, 2013
AIRIL BIN AHMAD

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PROPERTIES OF
CIRCLE
BY
MR.AIRIL AHMAD
AIRIL AHMAD

20. Friday, January 25, 2013
PROPERTIES OF CIRCLE
1. Angle subtended at the
circumference by the same
arc are equal.
AIRIL BIN AHMAD

21. Friday, January 25, 2013
PROPERTIES OF CIRCLE
ANGLE AT THE
CIRCUMFERENCE
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PROPERTIES OF CIRCLE
500
500
500
500
AIRIL BIN AHMAD

23. Friday, January 25, 2013
Example 1:
Find:
600
a. x = ………..
0
600
X0
y0 b. y0= ………..
300
AIRIL BIN AHMAD

24. Friday, January 25, 2013
Example 1:
Find:
300
0 600
a. x = ………..
y0
300
X0
600 b. y0= ………..
AIRIL BIN AHMAD

25. Friday, January 25, 2013
Example 2:
Find:
35 0 a. x0= ………..
y0
b. y0= ………..
z0
500
X 0
c. z0= ………..
AIRIL BIN AHMAD

26. Friday, January 25, 2013
Example 2:
Find:
350
a. x = ………..
0
350
X0
b. y0= ………..
z0
500
y0
c. z0= ………..
AIRIL BIN AHMAD

27. Friday, January 25, 2013
Example 2:
Find:
350
a. x = ………..
0
500
y0
500
z0
X0 b. y0= ………..
350
c. z0= ………..
AIRIL BIN AHMAD

28. Friday, January 25, 2013
Example 2:
Find:
350
a. x = ………..
0
350 y0
500
b. y0= ………..
Z0
X0 500
c. z0= ………..
AIRIL BIN AHMAD

29. Friday, January 25, 2013
Example 2:
Find:
Z
0 0 350
a. x = ………..
500 500
X
0
b. y0= ………..
Z0 = 1800 – 350 - 500
c. z0= ………..
Z0 = 950
AIRIL BIN AHMAD

30. Friday, January 25, 2013
Exercise
PAGE 48
EXERCISE 3.2A
NO. 1, 2 , 3
ENJOY DOING IT!!!
AIRIL BIN AHMAD

31. Friday, January 25, 2013
Exercise:  1.Find the value of x
a. b.
x0
320
200
x0
x0
AIRIL BIN AHMAD

32. Friday, January 25, 2013
Exercise:  1.Find the value of x
c. d.
420
x0
260
580
360
x0
AIRIL BIN AHMAD

33. Friday, January 25, 2013
2.Find the value of x and y
Exercise:

260
360
x0
AIRIL BIN AHMAD

34. Friday, January 25, 2013
AIRIL BIN AHMAD

35. Friday, January 25, 2013
PROPERTIES OF CIRCLE
2. An angle subtended at the
centre of a circle by an arc is
TWICE the angle subtended by
the arc at the circumference.
AIRIL BIN AHMAD

36. Friday, January 25, 2013
PROPERTIES OF CIRCLE
ANGLE AT THE
CIRCUMFERENCE
ANGLE AT THE
CENTRE
AIRIL BIN AHMAD

37. Friday, January 25, 2013
PROPERTIES OF CIRCLE
350
X0= 350x 2 = 700
700
X0
AIRIL BIN AHMAD

38. Friday, January 25, 2013
PROPERTIES OF CIRCLE
520
X0
X0= 1040 ÷ 2 = 520
1040
AIRIL BIN AHMAD

39. Friday, January 25, 2013
Example 1:
y0 x0= 3600-2500
x0= 1100
2500
y0= 1100 ÷ 2
X0 y0= 550
AIRIL BIN AHMAD

40. Friday, January 25, 2013
Example 2:
y0 x0= 1800-600
x0= 1200
y0= 1200 ÷ 2
X0 y0= 600
300 300
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41. Friday, January 25, 2013
Exercise
PAGE 52
EXERCISE 3.2C
NO. 1, 2 , 3
ENJOY DOING IT!!!
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42. Friday, January 25, 2013
A A B B C C D D E E
16 24 8 24 4 20 2 18 1 17
17 25 9 25 5 21 3 19 3 19
18 26 10 26 6 22 6 22 5 21
19 27 11 27 7 23 7 23 7 23
20 28 12 28 12 28 10 26 9 25
21 29 13 29 13 29 11 27 11 27
22 30 14 30 14 30 14 30 13 29
23 31 15 31 15 31 15 31 15 31
AIRIL BIN AHMAD

43. Friday, January 25, 2013
PROPERTIES OF CIRCLE
3. Angle subtended at the
circumference by the diameter
of a semicircle = 900
AIRIL BIN AHMAD

44. Friday, January 25, 2013
PROPERTIES OF CIRCLE
900
1800
AIRIL BIN AHMAD

45. Friday, January 25, 2013
Example 1:
X0 = 90 - 25
X0 = 650
900
x0 25 0 y0 = 90 - 38
380 y0 y0 = 520
900
AIRIL BIN AHMAD

46. Friday, January 25, 2013
Exercise
PAGE 53
EXERCISE 3.2D
NO. 1, 2 , 3
ENJOY DOING IT!!!
AIRIL BIN AHMAD

47. Friday, January 25, 2013
CYCLIC
QUADILATERAL
BY
MR.AIRIL AHMAD
AIRIL AHMAD

48. Friday, January 25, 2013
A cyclic quadrilateral is
a quadrilateral which is inscribed in a circle.
P
Q
S
R
PQRS is a cyclic quadrilateral. AIRIL BIN AHMAD

49. Friday, January 25, 2013
AIRIL BIN AHMAD

50. Friday, January 25, 2013
DEFINITION
A cyclic quadrilateral is a
quadrilateral with its four
vertices located on the
circumference of a circle
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51. Friday, January 25, 2013
a
b
a + c = 1800
b + d = 1800
d
c
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52. Friday, January 25, 2013
a b
e f
d c
h g
j k
q
n m r
t
s
AIRIL BIN AHMAD

53. Friday, January 25, 2013
 Exercise pg 58
 3.3c
 1b ,2 & 4
AIRIL BIN AHMAD

54. Friday, January 25, 2013
Exterior angles
and
the corresponding
interior angles
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55. Friday, January 25, 2013
If PQ is extended to M, then ∠RQM is an exterior angle.
P
Q
M
S
R
AIRIL BIN AHMAD

56. Friday, January 25, 2013
If SRM is a straight line,
which is the exterior angle?
P
Q
S
∠QRM is the exterior angle.
R M
AIRIL BIN AHMAD

57. Friday, January 25, 2013
For the exterior angle, ∠QRM.
Corresponding
interior P
opposite angle
Q
S
R
650 Exterior angle
Corresponding
interior angle
M
AIRIL BIN AHMAD

58. Friday, January 25, 2013
Homework
 Pg 61
 Ex.3.3e
 1, 2, 3, 4
AIRIL BIN AHMAD

59. Friday, January 25, 2013
Homework
 Pg 64
 Ex.3.3g
 1, 2, 3, 4
AIRIL BIN AHMAD