F. 4 Mathematics

Angles in a Circle

Yu Chun Keung Memorial College No.2

Chan K.B.(T1)

Content

Content

Main Menu

Review

Angle in semi-circle

Angle in the same segment

Exercise

What is the relationship between the a and b?

b = 2a

at centre twice at circumference

a

b

OHint : O is the centre.

Content

A BO

CGiven:

In a circle , O is centre.

AB is diameter

AOB = 180o

ACB = 90o

Content Next page

O

135

120

4575

150

105

165

9060

15 30

0

180

ProtractorM

ade in China

135

120

45

75

150

105

165

90

60

15

30

0

180

Prot

ract

or

Mad

e in

Chi

na

A B

CC’

ACB = ACB = AC ’B=90AC ’B=90oo

Content Next page Previous page

AB is a diameter. Find CAB.

A B

C

30

Solutions:

BCA = 90 ( ( in semi-circle )in semi-circle )

CAB + ABC + BCA = 180( ( s sum of s sum of ) )

CAB + 30 + 90 = 180

CAB = 60

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Given that AC = 6 and BC = 8. Find the radius of the circle.Solutions:

AB2 = AC 2 + BC 2

= 62 + 82

AB = 10

( the converse of in semi-circle ) A B

C

6 8Since BCA = 90, AB is a diameter.

radius = 10 2 = 5 Content

Previous page

IsIsACB = ACB = AC’B ?AC’B ?

Given:

AB is not a diameter, just a chord.

A B

C’

C

Content Next page

A B

C’

CWe try to rotateWe try to rotate

the the ABC’ABC’C’

C’C’

C’

C’

C’C’

C’C’C’

C’

Content Next page Previous page

A B

C’

C

O

AOB = 2 2 ACBACB

( at centre twice at circumference)

AOB = 2 2 AC’BAC’B

ACB= ACB= AC’BAC’B

O is the centre of circle

Content Next page Previous page

Find x.Solutions:

Besides, x = PQT

( sum of )

PQT = 180 QTP TPQ

P

R

Q

40

95 x

S

T= 180 95 40

= 45

( in same segment )

= 45

Content Next page Previous page

Given that TP = TS. Find y.Solutions:

( sum of ) TPS + TSP + QPT + SQP = 180

y + y + 55 + 45 = 180

2y = 80

( in same segment )

P

RQ

45

55y

S

T

QPR = QSR = 55.

Since TP = TS, TPS = TSP = y.

y = 40 Content Previous page

Question 1 Work Harder

Exercises

Question 2

Question 3

Question 4

Question 5

Ans 1

Ans 2

Ans 4

Ans 3

Ans 5

Content

B35

x

Exercise One

Find x .A

C

D

E

90

55

45

65

35

AB=8 and Radius=5. Find x .

6

4

8

5

10

8

5x

A

B

C

Exercise Two

A

B

C

D

E

30

x

Find x .

40

55

50

30

70

100

Exercise Three

C

A

E

B

D

60

x

Find x .

60

50

45

65

100

140

Exercise Four

E

A

C

D

B

Exercise Five

40

x

Find x .

90

55

45

50

40

D

A

C

B

E

Exercises

Wrong!!

Try Again

Exercises

Wrong!!

Try Again

Exercises

Wrong!!

Try Again

Exercises

Wrong!!

Try Again

Exercises

Correct !!

35

x

Exercise One

Find x .90

55

45

65

35 Exercises

A

B

C

D

E

AB=8 and Radius=5. Find x .

6

4

8

5

10

8

5x

A

B

C

Exercise Two

Exercises

A

B

C

D

E

30

x

Find x .

40

55

50

30

70

100

Exercise Three

Exercises

A

B

C

D

E

60

x

Find x .

60

50

45

65

100

140

Exercise Four

Exercises

A

B

C

D

E

Exercise Five

40

x

Find x .

90

55

45

50

40 Exercises

A

B

C

D

E