WorksheetsCIRCLE THEOREM
Total questions: 50
Worksheet time: 32mins
The radius through the midpoint of a chord bisects it at
180 degrees
a third
90 degrees
twice the angle at the circumference.
The angles in the same segment from a common chord are:
equal
30 degrees
add up to 90 degrees
doubled
The opposite angles in a cyclic quadrilateral
are equal
add up to 180 degrees
add up to 360 degrees
are 90 degrees
The angle between a radius and a tangent is _____________
180 degrees
90 degrees
Twice the angle at the centre
obtuse
The tangents to a circle from the same point will be
equal length
parallel
perpendicular
different lengths
How many degrees is angle a?
30
27
60
63
How many degrees is angle b ?
30
27
60
63
How many degrees is angle c ?
20
45
70
none of the above
How many degrees is angle d ?
20
45
70
none of the above
Find the value of the angle marked x....
50
100
80
90
Find the value of the angle marked x....
125
70
110
55
If the red angle is 140 degrees... calculate the green one.
30 degrees
40 degrees
50 degrees
70 degrees
Calculate x
262
98
252
49
Calculate y
49
98
196
262
Find the value of the angle marked x....
56
90
34
44
Find the value of the angle marked x....
90
43
47
53
Find the value of the angle marked x....
90
45
50
100
Find the value of the angle marked x....
76
38
152
14
Find the value of the angle marked x....
32
64
16
58
Find the value of the angle marked x....
88
75
92
102
A, B, C and D are points on the circumference on a circle.Find the size of angle DAB.
118
62
85
Find the value of the angle marked x....
61
63
117
119
Find the value of the angle marked x....
100
80
109
71
Find the value of the angle marked x....
102
51
129
78
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.
x=32 , y= 58
x=29, y=58
x=32 , y=32
DAE is a tangent to a circle.
Write down the size of angle ABC. Give the reason for your answer
61 , alternate segments
61 , same segments
63, alternate segments
ATB is a tangent to each circle with centre O. Find the size of each angle.
x = 34°
y = 11°
z = 15°
x = 65°
y = 69°
z = 46°
x = 46°
y = 69°
z = 65°
In the diagram, TP and TQ are tangents to a circle with centre O. Find each value of x
5x
90
15
180
In the diagram, TP and TQ are tangents to a circle with centre O. Find each value of x
80
45
90
180
extension
diagram shows a tangent to a circle with centre O. Find x and y in each case
x = 12°
y = 156°
x = 100°
y = 50°
x = 62°
y = 28
x = 30°
y = 60°
What is the size of the angle COA?
62
128
232
90
In the diagram, TP and TQ are tangents to a circle with centre O. Find each value of x
38
52
90
72
In the diagram, TP and TQ are tangents to a circle with centre O. Find each value of x
70
110
140
90
find m.
41
109
68
AC is a tangent to the circle at A and angle AOC = 63°.
Work out the size of angle ACO.
63
90
27
Shown is a circle with centre O.
ABC is a straight line.
Angle CBD is 146°.
Find the size of angle AOD.
86
68
34
RS is a tangent to the circle at R.
Calculate the value of x.
83
80
42
Find the shaded angle
(a)
Find the shaded angle
57
303
61.5
Find the shaded angle
58
64
32
Find the shaded angle
50
25
310
Find the size of each lettered angle
A= 65, b= 75, c=40
A= 75, b= 65, c=40
A= 40, b= 75, c=65
Find the size of each lettered angle
d=58, e=43, f=79
d=79, e=58, f=43
d=79, e=43, f=58
Find the size of each lettered angle
k=80, m=52, n=80
k=52, m=52, n=80
k=80, m=80, n=52
ATB is a tangent to each circle with centre O. Find the size of each angle.
x = 34°
y = 11°
z = 15°
x = 65°
y = 69°
z = 46°
x = 46°
y = 69°
z = 65°
Find the angle marked x in each of these circles with centre O.
180
149
62
31
Find the angle marked x in each of these circles with centre O.
10
90
80
180
