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