plumiCircle properties: Edexcel International GCSE Maths questions
Every Edexcel International GCSE Maths exam question on 4.6 Circle properties, 2019–2025, with its mark scheme and examiner’s report.
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All 43 questions on Circle properties, as a list
- June 2025 (R), Paper 1 Higher, Q23 (5 marks): Diagram NOT S accurately drawn P (3y − 5) cm (x + 2) cm T 4x cm (y + 3) cm Q R PTR and QTS are chords of a circle. PT = (3y – 5) cm QT = (y + 3) cm RT = 4x cm S
- June 2025 (R), Paper 2 Higher, Q15 (3 marks): A, B and C are points on a circle, centre O B Diagram NOT accurately drawn O 36° 21° A C Angle BAO = 36° Angle BCO = 21° Work out the size of angle ACO °
- June 2025, Paper 1 Foundation, Q3 (4 marks): Here is a prism. (a) How many faces has the prism? (b) How many vertices has the prism? O B A D C A and B are points on a circle, centre O (c) Write down the ma
- November 2024, Paper 2 Higher, Q16 (5 marks): A, B, C and D are points on a circle, centre O C Diagram NOT accurately drawn 54° B O 28° D A (a) (i) Work out the size of angle AOD º (ii) Give a reason for yo
- June 2024 (R), Paper 1 Higher, Q13 (5 marks): B Diagram NOT accurately drawn C 128° A O D A, B, C and D are points on a circle, centre O Angle BCD = 128° Work out the size of angle OBD Give a reason for eac
- November 2023, Paper 1 Foundation, Q3 (4 marks): (a) x Write down the mathematical name of the angle marked x P O P is a point on a circle with centre O (b) Write down the mathematical name of the line OP Here
- November 2023, Paper 1 Higher, Q14 (3 marks): Diagram NOT B accurately drawn O 52° A C A, B and C are points on a circle, centre O Angle OAC = 52° Find the size of angle ABC Give reasons for your working. °
- November 2023, Paper 1 Higher, Q22 (6 marks): [In this question 1 cm = 1 unit on the x-axis and 1 cm = 1 unit on the y-axis] P is a point on a circle with centre (0, 0) The coordinates of P are (8, -10) The
- June 2023 (R), Paper 2 Higher, Q18 (3 marks): Diagram NOT A accurately drawn B 16 cm 14 cm P 12 cm C D A, B, C and D are points on a circle. ABP and DCP are straight lines. AB = 16 cm BP = 14 cm CP = 12 cm
- June 2023 (R), Paper 2 Higher, Q20 (2 marks): A, B and C are points on a circle. B Diagram NOT accurately drawn A 78° N C M MN is the tangent to the circle at C AB = CB Angle BCN = 78° Find the size of angl
- June 2023, Paper 2 Foundation, Q23 (3 marks): Diagram NOT accurately drawn A O 48° C D A and C are points on a circle, centre O DA is the tangent to the circle at A and DC is the tangent to the circle at C
- June 2023, Paper 2 Higher, Q7 (3 marks): Diagram NOT accurately drawn A O 48° C D A and C are points on a circle, centre O DA is the tangent to the circle at A and DC is the tangent to the circle at C
- June 2023, Paper 2 Higher, Q14 (4 marks): S Diagram NOT accurately drawn R 22° O P Q P, Q, R and S are points on a circle, centre O ROP is a diameter of the circle. Angle PRQ = 22° (a) (i) Find the size
- January 2023 (R), Paper 2 Foundation, Q3 (4 marks): (a) Write down the mathematical name for an 8-sided polygon. x (b) What type of angle is the angle marked x? (c) On the diagram above, draw a chord of the circl
- January 2023 (R), Paper 2 Higher, Q23 (5 marks): AEC and BED are chords of a circle. B Diagram NOT accurately drawn A x cm (x + 5) cm 48° E (5x – 12) cm C (x + 12) cm D AE = (x + 5) cm BE = x cm CE = (5x – 12)
- January 2023, Paper 2 Higher, Q14 (5 marks): A, B, C and D are points on a circle, centre O EBF is the tangent to the circle at B A Diagram NOT 40° accurately drawn F O 66° B D C E (a) (i) Work out the siz
- June 2022 (R), Paper 1 Higher, Q15 (3 marks): R Q Diagram NOT S accurately drawn 136° O P P, Q, R and S are points on a circle with centre O PS is a diameter of the circle. Angle PQR = 136° Work out the siz
- June 2022 (R), Paper 2 Higher, Q20 (4 marks): The centre O of a circle has coordinates (4, 7) The point A, on the circle, has coordinates (6, 11) and AOP is a diameter of the circle. Find an equation of the
- January 2022 (R), Paper 1 Higher, Q14 (4 marks): B Diagram NOT accurately drawn 55° A C O D A, B, C and D are points on a circle, centre O AOC is a diameter of the circle. Angle BAC = 55° Work out the size of
- January 2022, Paper 1 Higher, Q16 (4 marks): The diagram shows a circle with centre O A B C Diagram NOT 55° accurately drawn O A, B and C are points on the circle so that the length of the arc ABC is 5 cm.
- January 2022, Paper 2 Higher, Q16 (4 marks): D, E, F and G are points on a circle, centre O Diagram NOT D accurately drawn G 42° O E F EOG is a diameter of the circle. Angle EGD = 42° Calculate the size of
- January 2022, Paper 2 Higher, Q19 (3 marks): S Diagram NOT accurately drawn 4 cm Q T 3 cm 12 cm P R PTQ is a diameter of a circle. RTS is a chord of the circle. TQ = 3 cm ST = 4 cm TR = 12 cm Calculate the
- November 2021, Paper 2 Higher, Q11 (3 marks): E Diagram NOT accurately drawn O F D 48° A B C B, D, E and F are points on a circle, centre O. ABC is a tangent to the circle. ODC is a straight line. BOE is a
- June 2021, Paper 1 Higher, Q15 (4 marks): P, Q and R are points on a circle, centre O. TRV is the tangent to the circle at R. Q V Diagram NOT 238° accurately drawn 60° O R P T Reflex angle POR = 238° An
- June 2021, Paper 2 Higher, Q18 (6 marks): B Diagram NOT 8 cm accurately drawn A 98° 7.5 cm 35° C D ABCD is a quadrilateral where A, B, C and D are points on a circle. AB = 8 cm BC = 7.5 cm Angle ABC = 9
- January 2021 (R), Paper 1 Higher, Q14 (4 marks): Diagram NOT E accurately drawn F 18° D 39° A C B B, D, E and F are points on a circle. ABC is the tangent at B to the circle. Angle ABD = 39° Angle EFD = 18° Wo
- January 2021, Paper 2 Higher, Q13 (3 marks): P, Q, R, S and T are points on a circle with centre O. Q Diagram NOT R accurately drawn m° P O 124° n° T S QOS is a diameter of the circle. angle POS = 124° ang
- November 2020 (R), Paper 1 Higher, Q15 (4 marks): E F Diagram NOT accurately drawn 40° D 70° A B C B, D, E and F are points on a circle. ABC is the tangent to the circle at B. Angle EDF = 40° Angle FBC = 70° Pr
- November 2020 (R), Paper 2 Higher, Q16 (3 marks): C B Diagram NOT accurately drawn A 40° D E A, B, C, D and E are points on a circle. Angle EAC = 40° (a) (i) Write down the size of angle EBC. ° (ii) Give a reas
- November 2020 (R), Paper 2 Higher, Q19 (4 marks): B Diagram NOT O accurately drawn 12 cm C A D A, B, C and D are points on a circle with centre O and radius 12 cm. The area of the sector OADC of the circle is 1
- November 2020 (R), Paper 2 Higher, Q26 (5 marks): A, B, D and E are points on a circle. ABC and EDC are straight lines. Diagram NOT A accurately drawn B (2 + 5 ) cm C 2 5 cm D E (4 + 5 ) cm BC = (2 + 5 ) cm ED
- November 2020, Paper 1 Higher, Q16 (4 marks): Diagram NOT accurately drawn N 58° O P M L L, M, N and P are points on a circle, centre O Angle MNP = 58° (a) (i) Find the size of angle MLP ° (ii) Give a reaso
- January 2020 (R), Paper 1 Higher, Q14 (4 marks): Diagram NOT B accurately drawn 38° O C A A, B and C are points on a circle, centre O. Angle ABC = 38° Work out the size of angle OAC. Give a reason for each sta
- January 2020 (R), Paper 2 Foundation, Q3 (2 marks): The diagram shows a line AB. A B (a) At the point A draw an acute angle. Label your acute angle a. The diagram shows a circle with centre O. O . (b) Draw a diam
- January 2020 (R), Paper 2 Higher, Q18 (2 marks): A Diagram NOT accurately drawn 9 cm 8 cm C P D 6 cm B APB and CPD are chords of a circle. AP = 9 cm PB = 6 cm CP = 8 cm Calculate the length of PD. cm
- January 2020, Paper 2 Higher, Q13 (4 marks): B 28° Diagram NOT C A accurately drawn 32° O D A, B, C and D are points on a circle, centre O. AOD is a diameter of the circle. Angle CBD = 28° Angle BDA = 32°
- June 2019 (R), Paper 1 Foundation, Q6 (3 marks): (a) The diagram shows a circle with centre O. B O A Write down the word from the box that describes the line AB. sector segment tangent chord diameter (b) The d
- June 2019 (R), Paper 1 Higher, Q23 (4 marks): C B Diagram NOT accurately drawn x 54° A F D 32° E B, C, D and F are points on a circle. ABC, AFD, BFE and CDE are straight lines. Work out the size of angle x.
- June 2019 (R), Paper 2 Higher, Q15 (4 marks): A, B, C and D are points on a circle, centre O. B Diagram NOT C accurately drawn O 98° A D AOC is a diameter of the circle. Angle AOD = 98° Work out the size of
- June 2019, Paper 1 Higher, Q20 (5 marks): B Diagram NOT accurately drawn A C V 71° D T A, B, C and D are points on a circle. TDV is the tangent to the circle at D. AB = AD Angle ADT = 71° Work out the s
- June 2019, Paper 2 Foundation, Q3 (3 marks): A, B and C'are points on a circle, centre O. AOC is a straight line. B (a) Write down the mathematical name for the line AC. (b) Write down the mathematical nam
- January 2019 (R), Paper 1 Higher, Q19 (5 marks): Diagram NOT accurately drawn E D C 73° A B B, C, D and E are points on a circle. AB is the tangent at B to the circle. AB is parallel to ED. Angle ABE = 73° Wor
- January 2019, Paper 2 Higher, Q20 (5 marks): Diagram NOT accurately drawn A D B x° P C Q A, B, C and D are points on a circle. PCQ is a tangent to the circle. AB = CB. Angle BCQ = x° Prove that angle CDA =
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