Non-Calculator

Q1.
Here is a cyclic quadrilateral.

x : y = 5 : 7

Work out the size of angle w.

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Answer _________________________________________ degrees

(Total 4 marks)

Page 1 of 18
AQA GCSE Maths - Circle Theorems (H) PhysicsAndMathsTutor.com
 Q2.
B, X, Y and Z are points on the circumference of a circle.
ABC is a tangent to the circle.
BX is parallel to ZY.

Not drawn accurately

Work out the size of angle ZXY.

You must show your working, which may be on the diagram.

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Answer ____________________________ degrees

(Total 3 marks)

Page 2 of 18
AQA GCSE Maths - Circle Theorems (H) PhysicsAndMathsTutor.com
 Q3.
A, B and C are points on a circle.

• BC bisects angle ABQ.

• PBQ is a tangent to the circle.

Not drawn accurately

Angle CBQ = x

Prove that AC = BC

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(Total 3 marks)

Page 3 of 18
AQA GCSE Maths - Circle Theorems (H) PhysicsAndMathsTutor.com
 Q4.
(a) A, B and C are points on the circumference of a circle with centre O.

Not drawn
accurately

Work out the size of angle x.

Answer ____________________________ degrees

(1)

(b) P, Q and R are points on the circumference of a circle with centre O.

Not drawn
accurately

Work out the size of angle y.

Give a reason for your answer.

Answer ____________________________ degrees

Reason ____________________________________________________________

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(2)
(Total 3 marks)

Page 4 of 18
AQA GCSE Maths - Circle Theorems (H) PhysicsAndMathsTutor.com
 Calculator

Q5.
ABCD is a cyclic quadrilateral.

Work out the values of x and y.

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x = ______________ , y = ______________
(Total 5 marks)

Page 5 of 18
AQA GCSE Maths - Circle Theorems (H) PhysicsAndMathsTutor.com
 Q6.
A, B and C are points on a circle.
CD is a tangent to the circle.

Write down the size of angle x.

Give a reason for your answer.

Answer ____________________ degrees

Reason _________________________________________
(Total 2 marks)

Page 6 of 18
AQA GCSE Maths - Circle Theorems (H) PhysicsAndMathsTutor.com
 Q7.
The diagram shows a cyclic quadrilateral ABCD.

ADE is a straight line.

CE is a tangent to the circle.

Work out the size of angle x.

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x = __________________________________ degrees
(Total 3 marks)

Page 7 of 18
AQA GCSE Maths - Circle Theorems (H) PhysicsAndMathsTutor.com
 Q8.
ABCD is a cyclic quadrilateral.

Not drawn accurately

Work out x and y.

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x = _____________________________________ degrees

y = _____________________________________ degrees
(Total 4 marks)

Page 8 of 18
AQA GCSE Maths - Circle Theorems (H) PhysicsAndMathsTutor.com
 Q9.
ABP and ADQ are tangents to the circle, centre O.
C lies on the circumference of the circle.

Prove that y = 2x

Give reasons for any statements you make.

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(Total 6 marks)

Page 9 of 18
AQA GCSE Maths - Circle Theorems (H) PhysicsAndMathsTutor.com
 Q10.
ABC and EDC are straight lines.
AD = ED

(a) Work out the size of angle AED.

Give a reason for your answer.

Answer ____________________________ degrees

Reason ____________________________________________________________

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(2)

(b) Work out x.

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Answer ____________________________ degrees

(4)
(Total 6 marks)

Page 10 of 18
AQA GCSE Maths - Circle Theorems (H) PhysicsAndMathsTutor.com
 Q11.
The diagram shows a circle, centre O.
AB is a tangent.

Not drawn
accurately

Work out the length OB.

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Answer ______________________________________ cm
(Total 4 marks)

Page 11 of 18
AQA GCSE Maths - Circle Theorems (H) PhysicsAndMathsTutor.com
 Q12.
A, B, C, D, E and F are points on a circle.

Circle the line that is a diameter of the circle.

BE AD AC BF

(Total 1 mark)

Page 12 of 18
AQA GCSE Maths - Circle Theorems (H) PhysicsAndMathsTutor.com
 Q13.
AB is a tangent to the circle.

Not drawn accurately

Write down the value of x.

Give a reason for your answer.

Answer ____________________________ degrees

Reason ________________________________________________________________
(Total 2 marks)

Page 13 of 18
AQA GCSE Maths - Circle Theorems (H) PhysicsAndMathsTutor.com
 Q14.
A, B, C, D and E are points on a circle.

AC is parallel to ED.

Not drawn accurately

(a) Write down the size of angle x.

Answer ____________________________ degrees

(1)

(b) Work out the size of angle y.

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Answer ____________________________ degrees

(3)
(Total 4 marks)

Page 14 of 18
AQA GCSE Maths - Circle Theorems (H) PhysicsAndMathsTutor.com
 Q15.
(a) P, Q, R and S are points on the circumference of the circle.
Not drawn accurately

Work out the size of angle x.

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Answer ___________________________________ degrees

(1)

(b) The diagram shows a circle and a tangent at T.

Not drawn accurately

Write down the size of angle w.

Give a reason for your answer.

Answer ___________________________________ degrees

Reason ___________________________________________________________
(2)

Page 15 of 18
AQA GCSE Maths - Circle Theorems (H) PhysicsAndMathsTutor.com
 (c) A, C and D are points on the circle, centre O.
BA and BC are tangents to the circle.
Not drawn accurately

Work out the size of the angle y.

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Answer ___________________________________ degrees

(3)
(Total 6 marks)

Page 16 of 18
AQA GCSE Maths - Circle Theorems (H) PhysicsAndMathsTutor.com
 Q16.
XTY is a tangent to the circle.
Not drawn
accurately

(a) Write down the value of x.

Give a reason for your answer.

Answer ___________________________________degrees

Reason ____________________________________________________________
(2)

(b) Work out the value of y.

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Answer ___________________________________degrees
(1)
(Total 3 marks)

Page 17 of 18
AQA GCSE Maths - Circle Theorems (H) PhysicsAndMathsTutor.com
 Q17.
A, B, C, D and E are points on a circle.

BFD and AFC are straight lines.

DC = DF

Work out the size of angle x.

You must show your working which may be on the diagram.

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Answer _________________________________________ degrees

(Total 4 marks)

Page 18 of 18
AQA GCSE Maths - Circle Theorems (H) PhysicsAndMathsTutor.com