Edexcel GCSE Maths

Topic Questions

Circle Theorems

1
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4 marks

q1-4-4-easy-edexcel-gcse-maths

B comma space C and D are points on the circumference of a circle, centre O.
A B and A D are tangents to the circle.

Angle D A B space equals space 50 degree

Work out the size of angle B C D.
Give a reason for each stage in your working.

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2
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5 marks

q2-4-4-easy-edexcel-gcse-maths

S and T are points on the circumference of a circle, centre O.
P T is a tangent to the circle.
S O P is a straight line.

Angle O P T equals space 32 degree

Work out the size of the angle marked x.
Give reasons for your answer.

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3
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3 marks

q3-4-4-easy-edexcel-gcse-maths

A comma space B and D are points on the circumference of a circle, centre O.
B O D is a diameter of the circle.
B C and A C are tangents to the circle.
Angle O C B space equals space 34 degree.

Work out the size of angle D O A.

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4
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4 marks

q4-4-4-easy-edexcel-gcse-maths

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

Angle A O C space equals space y.

Find the size of angle A B C in terms of y.
Give a reason for each stage of your working.

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5
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4 marks

q5-4-4-easy-edexcel-gcse-maths

A comma space B comma space C and D are points on the circumference of a circle, centre O.
B O D is a straight line.
Angle A C D space equals space 62 degree

Find the size of angle A D B.
Give a reason for each stage in your working.

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6
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5 marks

The points A comma space B comma space C and D lie on a circle.
C D E is a straight line.

q6-4-4-easy-edexcel-gcse-maths


B A space equals space B D
C B space equals space C D
Angle A B D space equals space 40 degree

Work out the size of angle A D E.
You must give a reason for each stage of your working.

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7
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4 marks

A B C D is a quadrilateral.

q23-paper-1h-nov-2020-aqa-gcse-maths

Prove that A B C D  is not a cyclic quadrilateral.

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8
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2 marks

A and B are points on a circle.

P A and P B are tangents.

q21a-paper-3h-nov-2020-aqa-gcse-maths

Work out the size of angle A P B.

.....................................degrees

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9
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2 marks

C comma space D and E are points on a circle.

X C equals X D.

q21b-paper-3h-nov-2020-aqa-gcse-maths

Is space X spacethe centre of the circle?
Tick a box.

square Yes            space square No

Show working to support your answer.

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10
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1 mark

AB and C are points on a circle.

D C B is a straight line.

P A Q is a tangent to the circle.

q22-paper-3h-june-2018-aqa-gcse-maths

Sam is trying to work out the size of angle m.
Here is his working.

      table row cell angle space A C B space end cell equals cell space 56 degree end cell row cell m space end cell equals cell space 180 degree space – space 56 degree end cell row cell m space end cell equals cell space 124 degree end cell end table

angles in the same segment are equal

angles at a point on a straight line add up to 180°

Make a criticism of his working.

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11
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2 marks

A comma space B and C are points on a circle.

C D is a tangent to the circle.

q19-paper3h-nov2017-aqa-gcse-maths

Write down the size of angle x.
Give a reason for your answer.

............................degrees 

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12
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2 marks

A comma space B comma space C comma space D comma space E and F are points on a circle.

q12-paper2h-june2017-aqa-gcse-maths

Circle the line that is a diameter of the circle.

B E A D A C B F

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13
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4 marks

In the diagram,

  • E, F and D are points on the circumference of the circle
  • G, D and H lie on a tangent to the circle
  • angle EFD = 55°
  • angle FDE = 43°.

q16b-paper6-nov2019-ocr-gcse-maths

Explain why angle HDF is 82°.

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14a
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2 marks

The diagram shows a circle, centre O.

Points A, B, C and D lie on the circumference of the circle.
EDF is a tangent to the circle.
Angle ABC = 82° and angle ODC = 57°.

q19-paper5-nov2018-ocr-gcse-maths

Work out the value of x.

x = ...................... 

14b
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3 marks

Work out the value of y.

y = ..................

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15a
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2 marks

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

q16-paper5-june2018-ocr-gcse-maths

PQ is a tangent to the circle at D.
Angle BDQ = 72° and angle ABD = 63°.

Work out angle x.
Give a reason for your answer.

Angle x = ...................° because ......................

15b
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2 marks

Work out angle y.
Give a reason for your answer.

Angle y = ...................° because .....................

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16a
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2 marks

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

q16-paper5-june2017-ocr-gcse-maths

Angle BAD = 52°.

Work out angle x.
Give a reason for your answer.

x = ................................... ° reason ..................................................................................

16b
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2 marks

Work out angle y.
Give a reason for your answer.

y = ................................... ° reason ..................................................................................

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17
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4 marks

D comma space E comma space F and G are points on a circle, centre O

q16-4ma1-2h-qp-jan22-paper2-igcse-maths

E O G is a diameter of the circle.

Angle E G D space equals space 42 degree

Calculate the size of angle D F G
Give a reason for each stage of your working.


Angle DFG = .......................................................

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