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Circle Theorems with reasons - Practice quiz.

Total questions: 10

Worksheet time: 15mins

Name
Class
Date
1.

A, B and C are points on the circumference of a circle, centre O.

Angle ABC = 430

a) Find the size of the angle AOC

angle AOC = ​ (a)  

b) Give a reason for your answer:

​ ​ (b)  

Choose from the below words
86
Center angle = twice the circumference angle.
Angles in the same segment are equal.
The angle in a semi-circle is always 90 degrees.
The angle in a semi-circle is always 90 degrees.
Tangents meet the radius at 90 degrees.
Alternate segment theorem.
Tangents which meet at an external point are equal
43
90
2.

B and D are points on the circumference of a circle, centre O

ABC is a tangent to the circle at B

a) Find the size of angle x

angle x = ​ ​ (a)  

b) Give a reason for your answer:

​ ​ ​ (b)   ​​

Choose from the below words
62
Tangents meet the radius at 90 degrees.
Angles in the same segment are equal.
The angle in a semi-circle is always 90 degrees.
The angle in a semi-circle is always 90 degrees.
Alternate segment theorem.
Tangents which meet at an external point are equal
28
90
Center angle = twice the circumference angle
3.

A, B, C and D are points on the circumference of a circle.

Angle BDC is 380 and one of the Angles at the intersection of the Chords BD and AC is 860 as indicated.

a) Find the size of angle BAC.

angle BAC = ​ ​ ​ (a)  

b) Give a reason for your answer:

​ ​ ​ (b)   ​​

Choose from the below words
38
Angles in the same segment are equal.
The angle in a semi-circle is always 90 degrees.
The angle in a semi-circle is always 90 degrees.
Alternate segment theorem.
Tangents which meet at an external point are equal
76
48
Center angle = twice the circumference angle
Tangents meet the radius at 90 degrees
4.

A, B, C and D are points on a circle.

Angle BAC = 400

Angle DBC = 55°.

a) Find the size of the angle DAC.

angle DAC = ​ ​ ​ ​ (a)  

b) Give a reason for your answer:

​ ​ ​ (b)   ​​

Choose from the below words
55
Angles in the same segment are equal.
The angle in a semi-circle is always 90 degrees.
The angle in a semi-circle is always 90 degrees.
Alternate segment theorem.
Tangents which meet at an external point are equal
40
95
Center angle = twice the circumference angle
Tangents meet the radius at 90 degrees
5.

A, B, C and D are points on a circle, centre O. AE is a tangent to the circle. Angle ADC = 68°

a) Find the size of angle ABC.

angle ABC = ​ ​ ​ ​ (a)  

b) Give a reason for your answer:

​ ​ ​ ​ (b)  

Choose from the below words
112
Opposite angles in a cyclic quad add to 180
The angle in a semi-circle is always 90 degrees.
The angle in a semi-circle is always 90 degrees.
Alternate segment theorem.
Tangents which meet at an external point are equal
136
68
Center angle = twice the circumference angle
Tangents meet the radius at 90 degrees
6.

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
7.

E, F, G and H are points on the circumference of a circle.

Angle HEF has a size of 990.

a) Find the size of angle FGH.

angle FGH = ​ ​ ​ ​ (a)  

b) Give a reason for your answer:

​ ​ ​ ​ (b)  

Choose from the below words
81
Opposite angles in a cyclic quad add to 180
The angle in a semi-circle is always 90 degrees.
The angle in a semi-circle is always 90 degrees.
Alternate segment theorem.
Tangents which meet at an external point are equal
80
50
Center angle = twice the circumference angle
Tangents meet the radius at 90 degrees
8.

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

a) Find the size of the angle x.

angle x = ​​ (a)   ​ ​ ​

b) Give a reason for your answer:

​ ​ ​ ​ (b)  

Choose from the below words
26
Triangle OQP is an Isosceles triangle.
The angle in a semi-circle is always 90 degrees.
Angles in the same segment are equal.
Triangle OQP is an equilateral triangle.
Tangents which meet at an external point are equal
52
Center angle = twice the circumference angle
Tangents meet the radius at 90 degrees
134
9.

A, B, C and D are points on a circle, centre O. AE is a tangent to the circle. Angle ADC = 68°

a) Find the size of angle AOC.

angle AOC = ​ ​ ​ ​ (a)  

b) Give a reason for your answer:

​ ​ ​ ​ ​ (b)  

Choose from the below words
136
Center angle = twice the circumference angle
The angle in a semi-circle is always 90 degrees.
The angle in a semi-circle is always 90 degrees.
Alternate segment theorem.
Tangents which meet at an external point are equal
68
Tangents meet the radius at 90 degrees
112
Opposite angles in a cyclic quad add to 180
10.

D, E, F, G and H are points on a circle. Angle EGH = 670

a) Find the size of angle EDH.

angle EDH = ​ ​ ​ ​ (a)  

b) Give a reason for your answer:

​ ​ ​ ​ (b)  

Choose from the below words
113
Opposite angles in a cyclic quad add to 180
The angle in a semi-circle is always 90 degrees.
The angle in a semi-circle is always 90 degrees.
Alternate segment theorem.
Tangents which meet at an external point are equal
67
134
Center angle = twice the circumference angle
Tangents meet the radius at 90 degrees