plumiCircle theorems: OCR GCSE Maths questions
Every OCR GCSE Maths exam question on G10 Circle theorems, 2017–2025, with its mark scheme and examiner’s report.
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All 17 questions on Circle theorems, as a list
- June 2025, Paper 4, Q13 (3 marks): A, B, and C are points on a circle, centre O. B Not to scale A 110° x° C O (a) Explain why OABC is not a cyclic quadrilateral. (b) Work out the value of x. x =
- November 2024, Paper 5, Q19 (5 marks): A, B, C and D are points on the circumference of a circle, centre O. BD is a diameter of the circle. EBF is a tangent to the circle. D C Not to scale O 25° 35°
- June 2024, Paper 4, Q12 (6 marks): (a) P, Q, R and S are points on the circumference of a circle, centre O. Angle SQR = 14 ° and angle SPQ = 62 ° . S Not to scale R O 14° 62° P Q Find the size of
- November 2023, Paper 5, Q22 (6 marks): In this question all angles are given in degrees. A, B, C and D are points on the circumference of a circle, centre O. A B Not to scale 4x – 150 O x + 20 D C (a
- November 2023, Paper 6, Q18 (4 marks): A, B and C are points on the circumference of a circle. A 8cm B Not to scale D 58° 45° C Points C and D lie on a tangent to the circle at C. Angle BCD 45 ° . =
- June 2023, Paper 4, Q17 (8 marks): (a) P, Q and R are points on the circumference of a circle, centre O. R 59° Not to scale Q 67° O T b a P S Angle PRQ = 59° and angle PQR = 67°. Line SPT is a ta
- November 2022, Paper 5, Q13 (3 marks): Points A, B, C and D lie on the circumference of a circle. Line AC intersects line BD at point E. B Not to scale A E D C Prove that triangle AED is similar to t
- June 2022, Paper 4, Q12 (7 marks): (a) Points A, B and C lie on the circumference of a circle. EAF is a tangent to the circle. B F Not to scale 53° 78° A 49° C E Write down the value of angle BCA
- November 2021, Paper 4, Q19 (9 marks): ABC is an isosceles triangle. The sides of the triangle ABC are all tangents to a circle of radius 6 cm, centre O. B Not to scale 6 cm O 70° A C Angle BAC = 70°
- November 2021, Paper 5, Q18 (5 marks): A, B, C and D are points on the circumference of a circle. EF is the tangent to the circle at D. Angle BDF = 70°. B Not to scale C A F 70° D E The ratio angle B
- November 2020, Paper 6, Q16 (5 marks): The diagram shows a circle, centre O. Points A, B and C lie on the circumference of the circle. Line AOB is a diameter. Line DAE is a tangent to the circle. Ang
- November 2019, Paper 6, Q16 (8 marks): (a) In the diagram, • A, B and C are points on the circumference of a circle • O is the centre of the circle • angle OAB = 15° • angle BCO = 10°. B Not to scale
- June 2019, Paper 5, Q16 (7 marks): A, B, C and D are points on the circumference of a circle, centre O. Angle BAD = 112° and angle DCO = 33°. B A y Not to scale 112° O z D 33° C (a) Show that ang
- November 2018, Paper 5, Q19 (5 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 OD
- June 2018, Paper 4, Q8 (5 marks): A, B, C and D are points on the circumference of a circle, centre O. C Not to scale 6.4 cm B O D 28° A Angle CAD = 28° and CD = 6.4 cm. BD is a diameter of the
- June 2018, Paper 5, Q16 (4 marks): A, B, C and D are points on the circumference of a circle. B 63° C y A x Not to scale 72° Q D P PQ is a tangent to the circle at D. Angle BDQ = 72° and angle AB
- June 2017, Paper 5, Q16 (4 marks): A, B, C and D are points on the circumference of a circle, centre O. B A Not to scale 52° O x y C D Angle BAD = 52°. (a) Work out angle x. Give a reason for you
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