Post on 24-Jan-2016
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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
Content Next page Previous page
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