WorksheetsCircle Theorems Activity
Total questions: 39
Worksheet time: 1hrs 18mins
What is this circle theorem
The sum of angles subtended by arc at centre and at circumference is equal to 90º
Angles subtended by arc at centre is twice the angle at circumference
Angles subtended by arc at circumference is twice the angle at centre
Angles subtended by the same arc are equal
Find the value of the angle marked x....
50
100
80
90
Find the value of the angle marked x....
125
70
110
55
What is this circle theorem
Angles subtended by the same arc are not equal
Angles subtended by arc at centre is twice the angle at circumference
Angles in alternate segments are equal
Angles subtended by the same arc are equal
Find the value of the angle marked x....
56
90
34
44
Find the value of the angle marked x....
88
44
92
46
What are the sizes of a and b?
a = 57, b = 114
a = 57, b = 57
a = 114, b = 57
a = 57, b = 28.5
What is this circle theorem
Sum of opposite angles in a cyclic quadrilateral is 180º
Sum of opposite angles in a cyclic quadrilateral is 360º
Sum of all the angles in a cyclic quadrilateral is 180º
All the angles in a cyclic quadrilateral is 90º
Which circle does not have cyclic quadrilateral?
Is OADC a cyclic quadrilateral?
No
Yes
∠x + ∠y =
45°
900°
180°
360°
x =
30°
40°
50°
60°
Find the sizes of the lettered angles in each of these circles
a = 50, b = 95
a = 85, b = 130
a = 95, b = 50
a = 130, b = 85
What is this circle theorem?
Angles subtended by an arc is 90º
An angle subtended at circumference by a semicircle is 180º
An angle subtended at circumference by a semicircle is 90º
The sum of angles of a triangle in a semicircle is 180º
Find the value of the angle marked x....
90
43
47
53
Find the value of the angle marked x....
90
45
50
100
What is this circle theorem?
An angle in a triangle inside a circle is 90º
The angle between the radius and the tangent is 90º
Angles in alternate segments are equal
Angles subtended by the same arc are equal
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
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
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
What is this circle theorem?
The perpendicular bisector of a chord is the radius
The tangent of a chord is the radius
The chord of a circle is the radius
The chord of a circle is the diameter
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?
They are the same
AX is bigger
XB is bigger
None of these answers
If XB=35cm what is the value of AX?
50cm
35cm
17.5cm
70cm
What is this circle theorem?
The angle between the perpendicular bisector of a chord and the tangent is 90º
The angle between the radius and tangent is 90º
The radius of a circle and the tangent at any point is parallel to each other
Tangents drawn from a circle has the same length as the radius
Determine y.
30
60
90
180
What is this circle theorem?
Two tangents drawn to a circle from a point are equal in length
The angle between two tangents drawn to a circle from a point is 90º
The angle between the tangent and the radius is 90º
The angle between two tangents drawn to a circle from a point is 180º
How would you solve this problem?
3x+1 = 6x-14
3x + 1 + 6x - 14 = 180
3x + 1 - 6x - 14 = 180
(3x + 1)(6x - 14)
Two tangents CD and CB intersect circle A. Find the length of the tangent segment BC.
2
3
9
14
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)
15
6
-24
14
Find the length of ST.
QS = 5
RT = 12
8
5
13
Cannot be determined.
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