Free Printable Circle Theorems

1.

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

a)

88

b)

75

c)

92

d)

102

2.

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

a)

90

b)

43

c)

47

d)

53

3.

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

a)

102

b)

51

c)

129

d)

78

4.

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

a)

56

b)

90

c)

34

d)

44

5.

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

a)

61

b)

63

c)

117

d)

119

6.

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

a)

90

b)

45

c)

50

d)

100

7.

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

a)

88

b)

44

c)

92

d)

46

8.

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

a)

35

b)

70

c)

55

d)

110

9.

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

a)

32

b)

64

c)

16

d)

58

10.

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

a)

41

b)

82

c)

164

d)

98

11.

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

a)

19

b)

38

c)

76

d)

52

12.

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

a)

76

b)

38

c)

152

d)

14

13.

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

a)

72

b)

144

c)

36

d)

90

14.

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

a)

65

b)

130

c)

90

d)

25

15.

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

a)

100

b)

80

c)

109

d)

71

16.

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

a)

50

b)

100

c)

80

d)

90

17.

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

a)

78

b)

88

c)

102

d)

92

18.

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

a)

106

b)

76

c)

74

d)

30

19.

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

a)

63

b)

126

c)

54

d)

90

20.

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

a)

125

b)

70

c)

110

d)

55

21.

What is the value of x and y?

a)

x=75°; y=93°

b)

x=65°;y=104°

c)

x=75°; y=94°

d)

x=65°; y=93

22.

What is the size of angle x?

a)

19^o

b)

76^o

c)

39^o

d)

38^o

23.

find the measure of angle a

a)

30

b)

21

c)

60

d)

120

24.

what are the values of c and d?

a)

c = 218, d = 71

b)

d = 109, c = 71

c)

c = 142, d = 218

d)

c = 142, d = 109

25.

What is the measure of angle c and d?

a)

c = 21, d = 50

b)

c = 63, d = 78

c)

c = 78, d = 63

d)

c = 10, d = 50

26.

What are the sizes of a and b?

a)

a = 57, b = 114

b)

a = 57, b = 57

c)

a = 114, b = 57

d)

a = 57, b = 28.5

27.

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

a)

90

b)

43

c)

47

d)

53

28.

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

a)

90

b)

45

c)

50

d)

100

29.

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

a)

50

b)

100

c)

80

d)

90

30.

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

a)

63

b)

126

c)

54

d)

90

31.

Work out the size of angle y - do not include units

(a)

32.

Work out the size of angle x - do not include units

(a)

33.

Work out the size of angle x - do not include units

(a)

34.

Work out the size of angle y - do not include units

(a)

35.

Work out the size of angle x - do not include units

(a)

36.

Work out the size of angle y - do not include units

(a)

37.

Work out the size of angle x - do not include units

(a)

38.

Work out the size of angle y - do not include units

(a)

39.

Work out the size of angle x - do not include units

(a)

40.

Work out the size of angle x - do not include units

(a)

41.

Work out the size of angle x - do not include units

(a)

42.

Work out the size of angle x - do not include units

(a)

43.

Work out the size of angle x - do not include units

(a)

44.

Work out the size of angle x - do not include units

(a)

45.

Work out the size of angle x - do not include units

(a)

46.

Work out the size of angle x - do not include units

(a)

47.

Work out the size of angle y - do not include units

(a)

48.

Work out the size of angle z - do not include units

(a)

49.

Work out the size of angle x - do not include units

Hint - find 5x first

(a)

50.

Work out the size of angle y - do not include units

(a)

51.

Work out the size of angle x - do not include units

(a)

52.

Find the size of angle B. You do not need to include units.

(a)

53.

Find the size of angle ACB.

(a)

54.

Find the size of angle DAB

(a)

55.

Find the size of x.

(a)

56.

Find the size of y.

(a)

57.

Find the size of angle x.

(a)

58.

Find the size of angle BCD.

(a)

59.

Find the angle POR.

(a)

60.

Find the angle ABC.

(a)

61.

Find the size of angle y.

(a)

62.

PA and PB are tangents of length 15cm to the circle with centre O. If PRO is a straight line with PR = 9cm, calculate the radius of the circle.

(a)

63.

SET is a tangent to the circle, centre O. Given that DE = DF and $\angle FET\ =\ 36\degree$ , calculate $\angle DES$

(a)

64.

Find the value of $b$

(a)

65.

ST and UT are tangents to the circle with centre O. OVT is a straight line. If $\angle SVT\ =\ 123\degree$ , calculate $\angle VST$

(a)

66.

What is the value of x?

(a)

67.

What is the value of x?

(a)

68.

What is the value of x?

(a)

69.

What is the value of angle ABC?

(a)

70.

What is the value of angle DOF?

(a)

71.

What is the value of angle IGH?

(a)

72.

What is the value of angle KLM?

(a)

73.

What is the value of angle QRS?

(a)

74.

In the diagram, a tangent and a line drawn to the point of tangency form a right triangle. Find the length of AO (the length of the hypotenuse)

a)

15

b)

6

c)

-24

d)

14

75.

Determine y.

a)

30

b)

60

c)

90

d)

180

76.

Assume both lines are tangent to circle O. What is the value of x?

a)

90

b)

115

c)

120

d)

45

77.

P, Q and R are points on the circumference of a circle, centre O.

PQ passes through O.

Angle RPQ = 67⁰.

a) Find the size of the angle PQR.

angle PQR = (a)

b) Give a reason for your answer:

(b)

Choose from the below words

23

The Angle in a semi-circle is always 90 degrees

Alternate segment theorem.

Tangents which meet at an external point are equal

67

Center angle = twice the circumference angle

Tangents meet the radius at 90 degrees

134

78.

Just write the answer with out the unit.

Give your answer to 1 decimal place.

(a)

79.

Leave out the units in your answer. correct to the nearest whole number.

(a)

80.

Calculate the value of x. Leave out the units in your answer. correct to the nearest whole number.

(a)

Circle Theorems

Total questions: 80

Worksheet time: 2hrs 40mins

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