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Circle Theorems Activity

Total questions: 39

Worksheet time: 1hrs 18mins

Name
Class
Date
1.

What is this circle theorem

a)

The sum of angles subtended by arc at centre and at circumference is equal to 90º

b)

Angles subtended by arc at centre is twice the angle at circumference

c)

Angles subtended by arc at circumference is twice the angle at centre

d)

Angles subtended by the same arc are equal

2.

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

a)

50

b)

100

c)

80

d)

90

3.
What is the m∠ADB?
a)
16o
b)
32o
c)
64o
d)
14o
4.
What is the m∠ACB?
a)
52o
b)
26o
c)
104o
d)
114o
5.
find the measure of angle a
a)
30
b)
21
c)
60
d)
120
6.

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

a)

125

b)

70

c)

110

d)

55

7.

What is this circle theorem

a)

Angles subtended by the same arc are not equal

b)

Angles subtended by arc at centre is twice the angle at circumference

c)

Angles in alternate segments are equal

d)

Angles subtended by the same arc are equal

8.
What is the size of angle x?
a)
19o
b)
76o
c)
39o
d)
38o
9.

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

a)

56

b)

90

c)

34

d)

44

10.

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

a)

88

b)

44

c)

92

d)

46

11.

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

12.

What is this circle theorem

a)

Sum of opposite angles in a cyclic quadrilateral is 180º

b)

Sum of opposite angles in a cyclic quadrilateral is 360º

c)

Sum of all the angles in a cyclic quadrilateral is 180º

d)

All the angles in a cyclic quadrilateral is 90º

13.

Which circle does not have cyclic quadrilateral?

a)
b)
c)
d)
14.

Is OADC a cyclic quadrilateral?

a)

No

b)

Yes

15.

∠x + ∠y =

a)

45°

b)

900°

c)

180°

d)

360°

16.

x =

a)

30°

b)

40°

c)

50°

d)

60°

17.

Find the sizes of the lettered angles in each of these circles

a)

a = 50, b = 95

b)

a = 85, b = 130

c)

a = 95, b = 50

d)

a = 130, b = 85

18.

What is this circle theorem?

a)

Angles subtended by an arc is 90º

b)

An angle subtended at circumference by a semicircle is 180º

c)

An angle subtended at circumference by a semicircle is 90º

d)

The sum of angles of a triangle in a semicircle is 180º

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.

What is this circle theorem?

a)

An angle in a triangle inside a circle is 90º

b)

The angle between the radius and the tangent is 90º

c)

Angles in alternate segments are equal

d)

Angles subtended by the same arc are equal

22.

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

23.

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

24.

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

25.

What is this circle theorem?

a)

The perpendicular bisector of a chord is the radius

b)

The tangent of a chord is the radius

c)

The chord of a circle is the radius

d)

The chord of a circle is the diameter

26.

MX is a line coming from the center and bisects the line AB at a right angle. What do you know about lines AX and XB?

a)

They are the same

b)

AX is bigger

c)

XB is bigger

d)

None of these answers

27.

If XB=35cm what is the value of AX?

a)

50cm

b)

35cm

c)

17.5cm

d)

70cm

28.
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
29.

What is this circle theorem?

a)

The angle between the perpendicular bisector of a chord and the tangent is 90º

b)

The angle between the radius and tangent is 90º

c)

The radius of a circle and the tangent at any point is parallel to each other

d)

Tangents drawn from a circle has the same length as the radius

30.

Determine y.

a)

30

b)

60

c)

90

d)

180

31.
What can you conclude from the picture?
a)
m is parallel to circle C
b)
m is skew to circle C
c)
m bisects circle C
d)
m is tangent to circle C
32.

What is this circle theorem?

a)

Two tangents drawn to a circle from a point are equal in length

b)

The angle between two tangents drawn to a circle from a point is 90º

c)

The angle between the tangent and the radius is 90º

d)

The angle between two tangents drawn to a circle from a point is 180º

33.

How would you solve this problem?

a)

3x+1 = 6x-14

b)

3x + 1 + 6x - 14 = 180

c)

3x + 1 - 6x - 14 = 180

d)

(3x + 1)(6x - 14)

34.

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

a)

2

b)

3

c)

9

d)

14

35.
What is the value of x?
a)
22
b)
25
c)
15
d)
20
36.

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

37.

Find the length of ST.

QS = 5

RT = 12

a)

8

b)

5

c)

13

d)

Cannot be determined.

38.

How do you feel about this topic?

a)
b)
c)
39.

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