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Worksheets

CIRCLE THEOREM

Total questions: 50

Worksheet time: 32mins

Name
Class
Date
1.

The radius through the midpoint of a chord bisects it at

a)

180 degrees

b)

a third

c)

90 degrees

d)

twice the angle at the circumference.

2.

The angles in the same segment from a common chord are:

a)

equal

b)

30 degrees

c)

add up to 90 degrees

d)

doubled

3.

The opposite angles in a cyclic quadrilateral

a)

are equal

b)

add up to 180 degrees

c)

add up to 360 degrees

d)

are 90 degrees

4.

The angle between a radius and a tangent is _____________

a)

180 degrees

b)

90 degrees

c)

Twice the angle at the centre

d)

obtuse

5.

The tangents to a circle from the same point will be

a)

equal length

b)

parallel

c)

perpendicular

d)

different lengths

6.

How many degrees is angle a?

a)

30

b)

27

c)

60

d)

63

7.

How many degrees is angle b ?

a)

30

b)

27

c)

60

d)

63

8.

How many degrees is angle c ?

a)

20

b)

45

c)

70

d)

none of the above

9.

How many degrees is angle d ?

a)

20

b)

45

c)

70

d)

none of the above

10.

Find the value of the angle marked x....

a)

50

b)

100

c)

80

d)

90

11.
If a is 600 , what is 2a ?
a)
300
b)
1200
c)
900
12.

Find the value of the angle marked x....

a)

125

b)

70

c)

110

d)

55

13.
What is the m∠ADB?
a)
16o
b)
32o
c)
64o
d)
14o
14.
find the measure of angle a
a)
30
b)
21
c)
60
d)
120
15.

If the red angle is 140 degrees... calculate the green one.

a)

30 degrees

b)

40 degrees

c)

50 degrees

d)

70 degrees

16.

Calculate x

a)

262

b)

98

c)

252

d)

49

17.

Calculate y

a)

49

b)

98

c)

196

d)

262

18.

Find the value of the angle marked x....

a)

56

b)

90

c)

34

d)

44

19.

Find the value of the angle marked x....

a)

90

b)

43

c)

47

d)

53

20.

Find the value of the angle marked x....

a)

90

b)

45

c)

50

d)

100

21.

Find the value of the angle marked x....

a)

76

b)

38

c)

152

d)

14

22.

Find the value of the angle marked x....

a)

32

b)

64

c)

16

d)

58

23.

Find the value of the angle marked x....

a)

88

b)

75

c)

92

d)

102

24.

A, B, C and D are points on the circumference on a circle.Find the size of angle DAB.

a)

118

b)

62

c)

85

25.

Find the value of the angle marked x....

a)

61

b)

63

c)

117

d)

119

26.

Find the value of the angle marked x....

a)

100

b)

80

c)

109

d)

71

27.

Find the value of the angle marked x....

a)

102

b)

51

c)

129

d)

78

28.

The points E, F and G lie on the circumference of a circle, centre O.

JGH is a tangent to the circle.

Find the value of x and the value of y.

a)

x=32 , y= 58

b)

x=29, y=58

c)

x=32 , y=32

29.

DAE is a tangent to a circle.

Write down the size of angle ABC. Give the reason for your answer

a)

61 , alternate segments

b)

61 , same segments

c)

63, alternate segments

30.

ATB is a tangent to each circle with centre O. Find the size of each angle.

a)

x = 34°

y = 11°

z = 15°

b)

x = 65°

y = 69°

z = 46°

c)

x = 46°

y = 69°

z = 65°

31.

In the diagram, TP and TQ are tangents to a circle with centre O. Find each value of x

a)

5x

b)

90

c)

15

d)

180

32.

In the diagram, TP and TQ are tangents to a circle with centre O. Find each value of x

a)

80

b)

45

c)

90

d)

180

33.

extension

diagram shows a tangent to a circle with centre O. Find x and y in each case

a)

x = 12°

y = 156°

b)

x = 100°

y = 50°

c)

x = 62°

y = 28

d)

x = 30°

y = 60°

34.

What is the size of the angle COA?

a)

62

b)

128

c)

232

d)

90

35.

In the diagram, TP and TQ are tangents to a circle with centre O. Find each value of x

a)

38

b)

52

c)

90

d)

72

36.

In the diagram, TP and TQ are tangents to a circle with centre O. Find each value of x

a)

70

b)

110

c)

140

d)

90

37.

find m.

a)

41

b)

109

c)

68

38.

AC is a tangent to the circle at A and angle AOC = 63°.

Work out the size of angle ACO.

a)

63

b)

90

c)

27

39.

Shown is a circle with centre O.

ABC is a straight line.

Angle CBD is 146°.

Find the size of angle AOD.

a)

86

b)

68

c)

34

40.

RS is a tangent to the circle at R.

Calculate the value of x.

a)

83

b)

80

c)

42

41.

Find the shaded angle

(a)  

42.

Find the shaded angle

a)

57

b)

303

c)

61.5

43.

Find the shaded angle

a)

58

b)

64

c)

32

44.

Find the shaded angle

a)

50

b)

25

c)

310

45.

Find the size of each lettered angle

a)

A= 65, b= 75, c=40

b)

A= 75, b= 65, c=40

c)

A= 40, b= 75, c=65

46.

Find the size of each lettered angle

a)

d=58, e=43, f=79

b)

d=79, e=58, f=43

c)

d=79, e=43, f=58

47.

Find the size of each lettered angle

a)

k=80, m=52, n=80

b)

k=52, m=52, n=80

c)

k=80, m=80, n=52

48.

ATB is a tangent to each circle with centre O. Find the size of each angle.

a)

x = 34°

y = 11°

z = 15°

b)

x = 65°

y = 69°

z = 46°

c)

x = 46°

y = 69°

z = 65°

49.

Find the angle marked x in each of these circles with centre O.

a)

180

b)

149

c)

62

d)

31

50.

Find the angle marked x in each of these circles with centre O.

a)

10

b)

90

c)

80

d)

180