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The Chinese University of Hong KongThe Chinese University of Hong Kong
EDD 5161FEDD 5161F
Educational Communications and Educational Communications and TechnologyTechnology
Group 14Group 14
MathematicsMathematics
Target Audience: F.4 Science StudentsTarget Audience: F.4 Science Students
Duration: 2Duration: 2 lessonslessons
Topic: Basic Properties of CirclesTopic: Basic Properties of Circles
Basic Properties of CirclesBasic Properties of Circles
Angles in the semi-circleAngles in the semi-circle
Angles in the same segmentAngles in the same segment
Basic terms of a circleBasic terms of a circle
Angles at centre and circumference
I.I. Basic Terms of a CircleBasic Terms of a Circle
A
B
C D
E
O
Chord
Radius
Diameter
Arc
Segment
II. Angles at centre and circumferenceII. Angles at centre and circumference
y = 2x
Reference: at centre = 2 at circumference
y
x
Proof:Proof:
m n
x y
x = 2m
y = 2n
x + y = 2 (m+n)
at centre = 2 ( at circumference)
Illustrative example:Illustrative example:
35 x
yO
Find x and y
70x
at centre twice at circumference
35y
at centre twice at circumference
Quiz:Quiz:
y
220
A.
B.
C.
D.
E.
8090
100110120
O
Q.1
O
120x
A.
B.
C.
D.
E.
4050
60
8070
Q.2
III.III. Angle in the semi-circleAngle in the semi-circle
90ABC
Reference: in the semi-circle
A
B
CO
Proof:Proof:
O
180A B
C 180AOB 90ACB
at centre twice at circumference
Illustrative example:Illustrative example:
zO
x 90x
in the semi-circle
2
90180 z ( base s, isos )
45z
IV.IV. Angle in the segmentAngle in the segment
x = y
Reference: in the same segment
x y
Proof:Proof:
Ox
z
y
z = 2x
at centre twice at circumference
z = 2y
at centre twice at circumference
x = y
Illustrative example:Illustrative example:
28
A
B
C
D
y
28BDC
in the same segment
90BCD
in the semi-circle
62y
sum of
O
Quiz:Quiz:
y
x
30
27
Find x and y
27x in the same segment
30y
in the same segment
Q.1
40x
A.
B.
C.
D.
E.
152535
4555
Q.2
Revision on the properties of circlesRevision on the properties of circles
y
x
A
B
CO
x y
in the same segment
in the semi-circle
at centre = 2 at circumference
TTHHEE EENNDD
Prepared byPrepared by
NameName Student No. Student No.
Chan Chi Man BenjaminChan Chi Man Benjamin 9804030098040300
Wong Kwong LeungWong Kwong Leung 9811894098118940
Chan Mei LingChan Mei Ling 9704370097043700