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Circle theorems: AQA GCSE Maths questions

Every AQA GCSE Maths exam question on G10 Circle theorems, 2017–2025, with its mark scheme and examiner’s report.

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1,304 questions

  1. Q15

    June 2025 · Paper 1H

    4 marksG10 Circle theorems
    The whole paper ↗
    June 2025 Paper 1H, question 15: A, C and D are points on a circle, diameter AC. ABC is an isosceles triangle with AC = BC BCD is a straight line. Work out the size of angle x. Not drawn accura

  2. Q23

    November 2024 · Paper 2H

    6 marksG10 Circle theoremsR4 Ratio notation
    The whole paper ↗
    November 2024 Paper 2H, question 23: (a) Not drawn accurately Line DAE is a tangent at A to the circle with centre O. Work out the size of angle x. x = ° 23 (b) Here is a cyclic quadrilateral. f :

  3. Q22

    June 2024 · Paper 1H

    3 marksG10 Circle theorems
    The whole paper ↗
    June 2024 Paper 1H, question 22: A, B and C are points on a circle, centre O. AP and BP are tangents to the circle. Work out the size of angle x. Not drawn accurately Answer °

  4. Q22

    November 2023 · Paper 1H

    3 marksG10 Circle theoremsR4 Ratio notation
    The whole paper ↗
    November 2023 Paper 1H, question 22: Here is a cyclic quadrilateral. a : b : c = 9 : 5 : 3 Work out the size of angle d. Not drawn accurately d = °

  5. Q16

    November 2023 · Paper 3H

    3 marksG10 Circle theoremsG20 Pythagoras and trigonometry
    The whole paper ↗
    November 2023 Paper 3H, question 16: PQ is a diameter of a circle. QR is a tangent to the circle. PQ = QR PR = 10 cm Work out the radius of the circle. Give your answer as a decimal. Not drawn accu

  6. Q20

    June 2023 · Paper 2H

    3 marksG10 Circle theorems
    The whole paper ↗
    June 2023 Paper 2H, question 20: (a) P, Q and R are points on a circle. S is a point inside triangle PQR. Assume that S is the centre of the circle. Work out the size of angle x. Not drawn accu

  7. Q26

    November 2022 · Paper 1H

    4 marksG10 Circle theorems
    The whole paper ↗
    November 2022 Paper 1H, question 26: P, Q and R are points on a circle. SP is a tangent to the circle. RQ = PQ Prove that y = 90° – x Not drawn accurately

  8. Q17

    November 2022 · Paper 3H

    3 marksG10 Circle theorems
    The whole paper ↗
    November 2022 Paper 3H, question 17: A, B and C are points on a circle, centre O. BD is a tangent to the circle. OCD is a straight line. Work out the size of angle x. Not drawn accurately x = degre

  9. Q18

    June 2022 · Paper 3H

    5 marksG10 Circle theorems
    The whole paper ↗
    June 2022 Paper 3H, question 18: A, B and C are points on a circle, centre O. DC is a tangent to the circle. Not drawn accurately Show that angle ABO : angle ACO = 3 : 1

  10. Q12

    November 2021 · Paper 2H

    3 marksG10 Circle theorems
    The whole paper ↗
    November 2021 Paper 2H, question 12: A, B and C are three points on a circle. The radii from A, B and C are shown. Not drawn accurately Is AC a diameter of the circle? You must show your working.

  11. Q29

    November 2021 · Paper 3H

    4 marksG10 Circle theoremsG6 Geometric proof
    The whole paper ↗
    November 2021 Paper 3H, question 29: A, B and C are three points on the circumference of a circle, centre O. BD and CD are tangents to the circle. ABDC is a kite. Angle BDC is x Prove that angle AB

  12. Q23

    November 2020 · Paper 1H

    4 marksG10 Circle theorems
    The whole paper ↗
    November 2020 Paper 1H, question 23: ABCD is a quadrilateral. Prove that ABCD is not a cyclic quadrilateral. Not drawn accurately

  13. Q21

    November 2020 · Paper 3H

    4 marksG10 Circle theorems
    The whole paper ↗
    November 2020 Paper 3H, question 21: (a) A and B are points on a circle. PA and PB are tangents. Work out the size of angle APB. Not drawn accurately Answer degrees 21 (b) C, D and E are points on

  14. Q25

    November 2019 · Paper 2H

    4 marksG10 Circle theorems
    The whole paper ↗
    November 2019 Paper 2H, question 25: C, D and E are points on a circle. CE = DE The tangent at D is shown. ACD and BCE are straight lines. Prove that y = 3x Not drawn accurately

  15. Q20

    June 2019 · Paper 1H

    5 marksG10 Circle theoremsG6 Geometric proof
    The whole paper ↗
    June 2019 Paper 1H, question 20: A, B and C are points on a circle. CD is a tangent. Not drawn accurately 20 (a) Assume that triangle ABC is isosceles with AC = BC Prove that AB is parallel to

  16. Q20

    November 2018 · Paper 1H

    4 marksG10 Circle theorems
    The whole paper ↗
    November 2018 Paper 1H, question 20: P, Q, R and S are points on a circle. PXR and QXS are straight lines. PX = SX Prove that QS is not a diameter of the circle. Not drawn accurately

  17. Q22

    June 2018 · Paper 3H

    1 markG10 Circle theorems
    The whole paper ↗
    June 2018 Paper 3H, question 22: A, B and C are points on a circle. DCB is a straight line. PAQ is a tangent to the circle. Not drawn accurately Sam is trying to work out the size of angle m. H

  18. Q24

    November 2017 · Paper 1H

    4 marksG10 Circle theorems
    The whole paper ↗
    November 2017 Paper 1H, question 24: Here is a cyclic quadrilateral. x : y = 5 : 7 Work out the size of angle w. Not drawn accurately Answer degrees

  19. Q19

    November 2017 · Paper 3H

    2 marksG10 Circle theorems
    The whole paper ↗
    November 2017 Paper 3H, question 19: 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 Not drawn

  20. Q19

    June 2017 · Paper 3H

    4 marksG10 Circle theoremsG3 Angles and polygons
    The whole paper ↗
    June 2017 Paper 3H, question 19: A, B, C, D and E are points on a circle. BFD and AFC are straight lines. DC = DF Not drawn accurately Work out the size of angle x. You must show your working w
All 21 questions on Circle theorems, as a list
  1. June 2025, Paper 1H, Q15 (4 marks): A, C and D are points on a circle, diameter AC. ABC is an isosceles triangle with AC = BC BCD is a straight line. Work out the size of angle x. Not drawn accura
  2. November 2024, Paper 2H, Q23 (6 marks): (a) Not drawn accurately Line DAE is a tangent at A to the circle with centre O. Work out the size of angle x. x = ° 23 (b) Here is a cyclic quadrilateral. f :
  3. June 2024, Paper 1H, Q22 (3 marks): A, B and C are points on a circle, centre O. AP and BP are tangents to the circle. Work out the size of angle x. Not drawn accurately Answer °
  4. November 2023, Paper 1H, Q22 (3 marks): Here is a cyclic quadrilateral. a : b : c = 9 : 5 : 3 Work out the size of angle d. Not drawn accurately d = °
  5. November 2023, Paper 3H, Q16 (3 marks): PQ is a diameter of a circle. QR is a tangent to the circle. PQ = QR PR = 10 cm Work out the radius of the circle. Give your answer as a decimal. Not drawn accu
  6. June 2023, Paper 2H, Q20 (3 marks): (a) P, Q and R are points on a circle. S is a point inside triangle PQR. Assume that S is the centre of the circle. Work out the size of angle x. Not drawn accu
  7. November 2022, Paper 1H, Q26 (4 marks): P, Q and R are points on a circle. SP is a tangent to the circle. RQ = PQ Prove that y = 90° – x Not drawn accurately
  8. November 2022, Paper 3H, Q17 (3 marks): A, B and C are points on a circle, centre O. BD is a tangent to the circle. OCD is a straight line. Work out the size of angle x. Not drawn accurately x = degre
  9. June 2022, Paper 3H, Q18 (5 marks): A, B and C are points on a circle, centre O. DC is a tangent to the circle. Not drawn accurately Show that angle ABO : angle ACO = 3 : 1
  10. November 2021, Paper 2H, Q12 (3 marks): A, B and C are three points on a circle. The radii from A, B and C are shown. Not drawn accurately Is AC a diameter of the circle? You must show your working.
  11. November 2021, Paper 3H, Q29 (4 marks): A, B and C are three points on the circumference of a circle, centre O. BD and CD are tangents to the circle. ABDC is a kite. Angle BDC is x Prove that angle AB
  12. November 2020, Paper 1H, Q23 (4 marks): ABCD is a quadrilateral. Prove that ABCD is not a cyclic quadrilateral. Not drawn accurately
  13. November 2020, Paper 3H, Q21 (4 marks): (a) A and B are points on a circle. PA and PB are tangents. Work out the size of angle APB. Not drawn accurately Answer degrees 21 (b) C, D and E are points on
  14. November 2019, Paper 2H, Q25 (4 marks): C, D and E are points on a circle. CE = DE The tangent at D is shown. ACD and BCE are straight lines. Prove that y = 3x Not drawn accurately
  15. June 2019, Paper 1H, Q20 (5 marks): A, B and C are points on a circle. CD is a tangent. Not drawn accurately 20 (a) Assume that triangle ABC is isosceles with AC = BC Prove that AB is parallel to
  16. November 2018, Paper 1H, Q20 (4 marks): P, Q, R and S are points on a circle. PXR and QXS are straight lines. PX = SX Prove that QS is not a diameter of the circle. Not drawn accurately
  17. June 2018, Paper 3H, Q22 (1 mark): A, B and C are points on a circle. DCB is a straight line. PAQ is a tangent to the circle. Not drawn accurately Sam is trying to work out the size of angle m. H
  18. November 2017, Paper 1H, Q24 (4 marks): Here is a cyclic quadrilateral. x : y = 5 : 7 Work out the size of angle w. Not drawn accurately Answer degrees
  19. November 2017, Paper 3H, Q19 (2 marks): 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 Not drawn
  20. June 2017, Paper 3H, Q19 (4 marks): A, B, C, D and E are points on a circle. BFD and AFC are straight lines. DC = DF Not drawn accurately Work out the size of angle x. You must show your working w
  21. Specimen, Paper 1H, Q21 (3 marks): A, B and C are points on a circle.  BC bisects angle ABQ.  PBQ is a tangent to the circle. Not drawn accurately A C P B Q x Angle CBQ = x Prove that AC = BC

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