1. Circle Theorems – Mixed – Higher – GCSE Questions
These questions are the same format as previous GCSE exams.
COPY means they use the exact same numbers as the original GCSE question.
Otherwise, they are clone questions using different numbers.
The worksheets are provided in a variety of sizes.

2. Printing To print handouts from slides -
Select the slide from the left. Then click:
File > Print > ‘Print Current Slide’
To print multiple slides -
Click on a section title to highlight all those slides,
or press ‘Ctrl’ at the same time as selecting slides to
highlight more than one. Then click:
File > Print > ‘Print Selection’
To print double-sided handouts -
Highlight both slides before using ‘Print Selection’.
Choose ‘Print on Both Sides’ and ‘Flip on Short Edge’.

3. GCSE GCSE Edexcel Higher: June 2017 Paper 2, Q15
A, B, C and D are four points on the circumference of a circle. 1
A, B, C and D are four points on the circumference of a circle. C C D D E E B B A A
AEC and DEB are straight lines.
Prove that triangle CED and triangle ABE are similar.
You must give reasons for each stage of your working.
AEC and DEB are straight lines.
Prove that triangle CED and triangle ABE are similar.
You must give reasons for each stage of your working.
(Total for Question 1 is 3 marks)
(Total for Question 1 is 3 marks)

5. GCSE GCSE Edexcel Higher: November 2017 Paper 3, Q20
A, B and C are points on the circumference of a circle, centre O.
AOC is a diameter of the circle.
Prove that angle ABC is 90°.
You must not use any circle theorems in your proof.
A, B and C are points on the circumference of a circle, centre O.
AOC is a diameter of the circle.
Prove that angle ABC is 90°.
You must not use any circle theorems in your proof.
(Total for Question 1 is 4 marks)
(Total for Question 1 is 4 marks)

7. GCSE GCSE Edexcel Higher : May 2018 Paper 1, Q11B 1 B C C O O A A
B and C are points on a circle, centre O.
BA is a tangent to the circle.
AOC is a straight line.
Angle OBC = x°.
Find the size of angle BAC, in terms of x.
Give your answer in its simplest form.
Give reasons for each stage of your working.
B and C are points on a circle, centre O.
BA is a tangent to the circle.
AOC is a straight line.
Angle OBC = x°.
Find the size of angle BAC, in terms of x.
Give your answer in its simplest form.
Give reasons for each stage of your working.
(Total for Question 1 is 5 marks)
(Total for Question 1 is 5 marks)

9. GCSE GCSE Edexcel Higher: June 2018 Paper 2, Q13O O B B E 𝑥° E 𝑥° 𝑦° 𝑦° D D A A F F
A, B, C and D are points on the circumference of a circle, centre O.
EAF is a tangent to the circle.
Show that y – x = 90°
You must give a reason for each stage of your working.
A, B, C and D are points on the circumference of a circle, centre O.
EAF is a tangent to the circle.
Show that y – x = 90°
You must give a reason for each stage of your working.
(3)
(3)
Jack was asked to give some possible values for x and y.
He said,
“y could be 200 and x could be 110 because 200 – 110 = 90”
(b) Is Jack correct?
You must give a reason for your answer.
Jack was asked to give some possible values for x and y.
He said,
“y could be 200 and x could be 110 because 200 – 110 = 90”
(b) Is Jack correct?
You must give a reason for your answer.
(1)
(1)
(Total for Question 1 is 4 marks)
(Total for Question 1 is 4 marks)

11. GCSE Edexcel Higher: June 2017 Paper 2, Q15
A, B, C and D are four points on the circumference of a circle. C D E B A
AEC and DEB are straight lines.
Prove that triangle CED and triangle ABE are similar.
You must give reasons for each stage of your working.
(Total for Question 1 is 3 marks)

12. GCSE Edexcel Higher: November 2017 Paper 3, Q20
A, B and C are points on the circumference of a circle, centre O.
AOC is a diameter of the circle.
Prove that angle ABC is 90°.
You must not use any circle theorems in your proof.
(Total for Question 1 is 4 marks)

13. GCSE Edexcel Higher : May 2018 Paper 1, Q11 1 B C O A
B and C are points on a circle, centre O.
BA is a tangent to the circle.
AOC is a straight line.
Angle OBC = x°.
Find the size of angle BAC, in terms of x.
Give your answer in its simplest form.
Give reasons for each stage of your working.
(Total for Question 1 is 5 marks)

14. GCSE Edexcel Higher: June 2018 Paper 2, Q13 1 C O B 𝑥° E 𝑦° D A F
A, B, C and D are points on the circumference of a circle, centre O.
EAF is a tangent to the circle.
Show that y – x = 90°
You must give a reason for each stage of your working.
(3)
Jack was asked to give some possible values for x and y.
He said,
“y could be 200 and x could be 110 because 200 – 110 = 90”
(b) Is Jack correct?
You must give a reason for your answer.
(1)
(Total for Question 1 is 4 marks)

15. < < BEA = CED < < ACD = ABD < < BAC = BDC GCSE X Y X
Edexcel Higher: June 2017 Paper 2, Q15 1
A, B, C and D are four points on the circumference of a circle. X C Y D E B X Y A
AEC and DEB are straight lines.
Prove that triangle CED and triangle ABE are similar.
You must give reasons for each stage of your working.
<
<
Vertically opposite angles are equal.
BEA = CED
<
<
ACD = ABD
Angles in the same segment are equal
<
<
BAC = BDC
All angles are the same, so the two triangles are similar
(Total for Question 1 is 3 marks)

16. y x GCSE GCSE 180 −𝑦 2 180 − 𝑥 2 a + a + b + b = 180° 2a + 2b = 180°
Edexcel Higher: November 2017 Paper 3, Q20
Edexcel Higher: November 2017 Paper 3, Q20
180 −𝑦 2 1 C 1 C B a B b y b a a b
180 − 𝑥 2 x O O b a A A
A, B and C are points on the circumference of a circle, centre O.
AOC is a diameter of the circle.
Prove that angle ABC is 90°.
You must not use any circle theorems in your proof.
A, B and C are points on the circumference of a circle, centre O.
AOC is a diameter of the circle.
Prove that angle ABC is 90°.
You must not use any circle theorems in your proof.
<
<
AOB = x
AOC = y
Angles at the base of an isosceles triangle are equal.
Angles at base of isosceles triangle are equal.
Interior angles of a triangle total 180°
<
ABO = a = 180 − 𝑥 2 =90− 𝑥 2
a + a + b + b = 180°
<
CBO = b = 180 − 𝑦 2 =90− 𝑦 2
2a + 2b = 180°
CBA = a + b = 90− 𝑥 − 𝑦 2 =180 − 𝑥 2 − 𝑦 2
<
a + b = 90°
=180 − 𝑥 2 + 𝑦 2
Therefore, angle ABC = 90°
𝑥+𝑦=180°
Angles on a straight line total 180°.
=180 − 𝑥+𝑦 2
<
CBA = 180 − = 90°
(Total for Question 1 is 4 marks)
(Total for Question 1 is 4 marks)

17. Base angles in isosceles triangles are equal
GCSE
Edexcel Higher : May 2018 Paper 1, Q11 1 B 𝑥
90° 𝑥 C O
𝐵𝐴𝐶 A
B and C are points on a circle, centre O.
BA is a tangent to the circle.
AOC is a straight line.
Angle OBC = x°.
Find the size of angle BAC, in terms of x.
Give your answer in its simplest form.
Give reasons for each stage of your working.
Angle OCB = 𝑥
Base angles in isosceles triangles are equal
Angle CBA = 𝑥 + 90
Tangent to a circle is perpendicular
to the radius
180 = BAC 𝑥 + 𝑥
Angles in a triangle total 180°
Rearrange
BAC = 90 – 2𝑥
(Total for Question 1 is 5 marks)

18. GCSE Angle CAE = y (alternate segment theorem)
Edexcel Higher: June 2018 Paper 2, Q13 1 C O B E 𝑦° 𝑥° 𝑦° D A
90° F
A, B, C and D are points on the circumference of a circle, centre O.
EAF is a tangent to the circle.
Show that y – x = 90°
You must give a reason for each stage of your working.
Angle CAE = y (alternate segment theorem)
Angle EAO = (tangent to a circle is
perpendicular to the radius)
y = 90 + x
y - x = 90
(3)
Jack was asked to give some possible values for x and y.
He said,
“y could be 200 and x could be 110 because 200 – 110 = 90”
(b) Is Jack correct?
You must give a reason for your answer.
No, y is an angle inside a triangle and
must be less than 180.
(1)
(Total for Question 1 is 4 marks)

19. tom@goteachmaths.co.uk Questions? Comments? Suggestions?
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