Free Printable Circle Theorems

1.

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

2.

What is the size of angle x?

a)

19^o

b)

76^o

c)

39^o

d)

38^o

3.

find the measure of angle a

a)

30

b)

21

c)

60

d)

120

4.

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

5.

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

6.

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

7.

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

a)

90

b)

43

c)

47

d)

53

8.

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

a)

90

b)

45

c)

50

d)

100

9.

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

a)

50

b)

100

c)

80

d)

90

10.

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

a)

63

b)

126

c)

54

d)

90

11.

Which is the correct way to solve this?

a)

3x+13=-3+5x

b)

3x+13+19.3=-3+5x

c)

(3x+13)(-3+5x)=19.3

d)

3x+13+-3+5x=19.3

12.

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

13.

find the measure of angle a

a)

30

b)

21

c)

60

d)

120

14.

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

15.

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

16.

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

a)

90

b)

43

c)

47

d)

53

17.

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

a)

63

b)

126

c)

54

d)

90

18.

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

a)

102

b)

51

c)

129

d)

78

19.

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

a)

56

b)

90

c)

34

d)

44

20.

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

a)

41

b)

82

c)

164

d)

98

21.

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

a)

125

b)

70

c)

110

d)

55

22.

a)

w = 26⁰, x = 128⁰ and y = 52⁰

b)

w = 52⁰, x = 128⁰ and y = 26⁰

c)

w = 26⁰, x = 128⁰ and y = 64⁰

d)

w = 52⁰, x = 128⁰ and y = 64⁰

23.

Calculate the values of p, q and r.

a)

p = 54⁰, q = 51⁰ and r = 78⁰

b)

p = 54⁰, q = 78⁰ and r = 51⁰

c)

p = 54⁰, q = 75⁰ and r = 78⁰

d)

p = 54⁰, q = 51⁰ and r = 75⁰

24.

Calculate angles DBA and DAB.

a)

DBA = 20⁰ and DAB = 62⁰

b)

DBA = 62⁰ and DAB = 98⁰

c)

DBA = 20⁰ and DAB = 98⁰

d)

DBA = 20⁰ and DAB = 82⁰

25.

Find angles ACD and ADB.

a)

ACD = 34⁰ and ADB = 32⁰

b)

ACD = 58⁰ and ADB = 34⁰

c)

ACD = 34⁰ and ADB = 32⁰

d)

ACD = 58⁰ and ADB = 32⁰

26.

a)

52⁰

b)

38⁰

c)

76⁰

d)

104⁰

27.

Find the values of angles t, y and z.

a)

t = 10⁰, y = 40⁰ and z = 80⁰

b)

t = 10⁰, y = 50⁰ and z = 40⁰

c)

t = 20⁰, y = 40⁰ and z = 50⁰

d)

t = 10⁰, y = 80⁰ and z = 40⁰

28.

Two tangents CD and CB intersect circle A. Find the length of the tangent segment BC.

a)

2

b)

3

c)

9

d)

14

29.

In the diagram, the diameter of the circle is perpendicular to the chord. Solve for the value of "x"

a)

26

b)

24

c)

30

d)

20

30.

Determine x.

a)

32

b)

16

c)

64

d)

21

31.

The angle in a semi-circle is ___________

a)

$180^0$

b)

$90^0$

c)

$360^0$

d)

equal

32.

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

a)

90

b)

43

c)

47

d)

53

33.

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

a)

90

b)

45

c)

50

d)

100

34.

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

a)

equal

b)

30 degrees

c)

add up to 90 degrees

35.

What is the size of angle x?

a)

19^o

b)

76^o

c)

39^o

d)

38^o

36.

The angle at the centre (y) is _______ the angle (x) at the circumference.

a)

twice

b)

half

c)

equal to

d)

90 degrees

37.

find the measure of angle a

a)

30

b)

21

c)

60

d)

120

38.

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

39.

What best describes segment AB?

a)

chord

b)

secant

c)

tangent

d)

diameter

40.

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.

41.

If O is the centre of the circle, find the radius of the circle given that XY = 16cm and OM = 15cm.

a)

17 cm

b)

16 cm

c)

15 cm

d)

14 cm

42.

Solve for x

a)

6

b)

7

c)

8

d)

9

43.

The angle between a radius and a tangent is _____________

a)

180 degrees

b)

90 degrees

c)

Twice the angle at the centre

d)

obtuse

44.

The tangents to a circle from the same point will be

a)

equal length

b)

parallel

c)

perpendicular

d)

different lengths

45.

Find the length of BC.

a)

2

b)

3

c)

9

d)

14

46.

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

47.

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

48.

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

49.

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

a)

102

b)

51

c)

129

d)

78

50.

Which other angle in the diagram is 75 degrees?

a)

A

b)

B

c)

C

d)

D

51.

Which is the correct way to solve this?

a)

x=(360-110)/2

b)

x=110/2

c)

x=(250-110)/2

d)

x=(250+110)/2

52.

Which is the correct way to solve this?

a)

70=(180+x)/2

b)

70=(180-x)/2

c)

x=(180+70)/2

d)

x=(180-70)/2

53.

Which is the correct way to solve this?

a)

x=(142-72)/2

b)

x=(142+72)/2

c)

72=(142-x)/2

d)

72=(142+x)/2

54.

Which is the correct way to solve this?

a)

x=(62-50)/2

b)

x=(62+50)/2

c)

50=(62+x)/2

d)

62=(50+x)/2

55.

Which is the correct way to solve this?

a)

210=x/2

b)

x=210/2

c)

x=150/2

d)

150=x/2

56.

Which is the correct way to solve this?

a)

x=284/2

b)

284=x/2

c)

x=76/2

d)

76=x/2

57.

Which is the correct way to solve this?

a)

8x=12

b)

12x=8

c)

8(x+8)=12

d)

8(x+8)=12(12)

58.

Which is the correct way to solve this?

a)

x(x+14)=12(33)

b)

14x=12(21)

c)

12x=14(21)

d)

21x=(12)(14)

59.

Which is the correct way to solve this?

a)

7x=6(8)

b)

7(x+7)=6(14)

c)

6x=7(8)

d)

7(14)=6(6+x)

60.

Which is the correct way to solve this?

a)

3x+13=-3+5x

b)

3x+13+19.3=-3+5x

c)

(3x+13)(-3+5x)=19.3

d)

3x+13+-3+5x=19.3

61.

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

(a)

62.

Find the size of angle ACB.

(a)

63.

Find the size of angle DAB

(a)

64.

Find the size of x.

(a)

65.

Find the size of y.

(a)

66.

Find the size of angle x.

(a)

67.

Find the size of angle BCD.

(a)

68.

Find the angle POR.

(a)

69.

Find the angle ABC.

(a)

70.

Find the size of angle y.

(a)

71.

If O is the centre of the circle, find the radius of the circle given that XY = 16cm and OM = 15cm.

(a)

72.

Find the value of x.

(a)

73.

Find the value of x.

(a)

74.

The cross-section of a railway tunnel is the major segment APB of the circle, centre O, as shown in the diagram. Given that OA = OB = 3cm, $\angle AOB\ =\ 80\degree\$ and taking $\pi$ to be 3.142, calculate the area of the major segment APB.

(a)

75.

In the figure, PT is a tangent to the circle, centre O and POS is a diameter. The radius OR is parallel to PT, the line TO cuts the circle at Q and $\angle OTP\ =\ 36\degree$

Find $\angle QSR$

(a)

76.

The chords EH and FG of the circle are produced to meet at X. Given that $\angle EGH\ =\ 40\degree$ and XH = HF = FE, calculate $\angle HXG$

(a)

77.

Find the value of $x$

(a)

78.

Find the value of $x$

(a)

79.

In the circle, the diameter QS intersects the chord PR at M, the midpoint of PR. Given that O is the centre of the circle and $\angle POQ\ =\ 136\degree$ , calculate $\angle RSQ$

(a)

80.

TV is a diameter of the circle. Given that UW = UV and $\angle VUW\ =\ 30\degree$ , calculate $\angle UVT$

(a)

81.

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)

82.

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

(a)

83.

Find the value of $b$

(a)

84.

Find the size of angle $b$

(a)

85.

Find the size of angle $x$

(a)

86.

ABCD is a cyclic quadrilateral with AD = AB and AD is produced to E. If $\angle CDE\ =\ 70\degree$ and $\angle CDB\ =\ 72\degree$ , calculate $\angle BAD$

(a)

87.

EFGH is a cyclic quadrilateral with EH parallel to FG. DG is a diameter of the circle, centre O. Given that $\angle DOH\ =\ 82\degree$ and $\angle DGE\ =\ 17\degree$ , calculate $\angle HEG$

(a)

88.

A, B, C, D and E are points on a circle. AB = AE, $\angle EAB\ =\ 130\degree$ and $\angle EDC\ =\ 110\degree$ , calculate $\angle ABC$

(a)

89.

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)

90.

TKXM and SNXL are two tangents to one of the circles in the diagram. JKL is a straight line. Given that $\angle TKJ\ =\ 54\degree$ and $\angle NJK\ =\ 40\degree$ , calculate $\angle LMN$

(a)

91.

What is this line called?

a)

Radius

b)

Diameter

c)

Chord

d)

Arc

92.

What is this called?

a)

Radius

b)

Chord

c)

Diameter

d)

Circumference

93.

The diameter is (a) the radius.

94.

I am called a...

a)

Chord

b)

Tangent

c)

Arc

d)

Line

95.

What is this called?

a)

Diameter

b)

Radius

c)

Chord

d)

Sector

96.

I am a...

a)

Slice

b)

Sector

c)

Tangent

d)

Segment

97.

I am a...

a)

Sector

b)

Segment

c)

Slice

d)

Piece

98.

Find the angle a.

a)

35 degrees

b)

125 degrees

c)

180 degrees

99.

Find the angle b.

a)

50 degrees

b)

90 degrees

c)

140 degrees

100.

Find the angle c.

a)

175 degrees

b)

85 degrees

c)

35 degrees

Circle Theorems

Total questions: 100

Worksheet time: 1hrs 23mins

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