1. Circle Theorems – Alternate Segment – Higher – GCSE Questions – AQA
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 2 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. AQA Higher: November 2017 Paper 3, Q19
A, B and C are points on a circle.
DA is a tangent to the circle. 1
A, B and C are points on a circle.
DA is a tangent to the circle. A B A B
44°
44° 𝑥
88° 𝑥
Not drawn
accurately
Not drawn
accurately
88°
48°
48° D D C C
Write down the size of angle 𝑥.
Give a reason for your answer.
Write down the size of angle 𝑥.
Give a reason for your answer.
[2 marks]
[2 marks]
Answer
degrees
Answer
degrees
Reason
Reason
AQA Higher: November 2017 Paper 3, Q19
AQA Higher: November 2017 Paper 3, Q19 1
A, B and C are points on a circle.
DA is a tangent to the circle. 1
A, B and C are points on a circle.
DA is a tangent to the circle. A B A B 𝑥
44°
88° 𝑥
44°
Not drawn
accurately
Not drawn
accurately
88°
48°
48° D D C C
Write down the size of angle 𝑥.
Give a reason for your answer.
Write down the size of angle 𝑥.
Give a reason for your answer.
[2 marks]
[2 marks]
Answer
degrees
Answer
degrees
Reason
Reason

5. AQA Higher: June 2018 Paper 3, Q22 AQA Higher: June 2018 Paper 3, Q22
A, B and C are points on a circle.
DCB is a straight line.
PAQ is a tangent to the circle. 1
A, B and C are points on a circle.
DCB is a straight line.
PAQ is a tangent to the circle.
Not drawn
accurately
Not drawn
accurately Q Q B B C C D D 𝑚° 𝑚°
56°
56° A A P P
Sam is trying to work out the size of angle 𝑚.
Here is his working.
Sam is trying to work out the size of angle 𝑚.
Here is his working.
angle ACB = 56° angles in the same segment are equal
𝑚 = 180° – 56° angles at a point on a straight line add up to 180°
𝑚 = 124°
angle ACB = 56° angles in the same segment are equal
𝑚 = 180° – 56° angles at a point on a straight line add up to 180°
𝑚 = 124°
Make a criticism of his working.
Make a criticism of his working.
[1 mark]
[1 mark]

8. AQA Higher: June 2018 Paper 3, Q22
A, B and C are points on a circle.
DCB is a straight line.
PAQ is a tangent to the circle.
Not drawn
accurately Q B C D 𝑚°
56° A P
Sam is trying to work out the size of angle 𝑚.
Here is his working.
angle ACB = 56° angles in the same segment are equal
𝑚 = 180° – 56° angles at a point on a straight line add up to 180°
𝑚 = 124°
Make a criticism of his working.
[1 mark]

10. Should be ‘Alternate Segment’ stated
AQA Higher: June 2018 Paper 3, Q22 1
A, B and C are points on a circle.
DCB is a straight line.
PAQ is a tangent to the circle.
Not drawn
accurately Q B C D 𝑚°
56° A P
Sam is trying to work out the size of angle 𝑚.
Here is his working.
angle ACB = 56° angles in the same segment are equal
𝑚 = 180° – 56° angles at a point on a straight line add up to 180°
𝑚 = 124°
Make a criticism of his working.
[1 mark]
Should be ‘Alternate Segment’ stated

11. tom@goteachmaths.co.uk Questions? Comments? Suggestions?
…or have you found a mistake!?
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