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Geometry Worksheets with Circle Theorems - Higher GCSE Questions

Assorted geometry questions involving circle theorems for Higher GCSE level, formatted like real exam questions. Includes proving triangle similarities, angle calculations, and more. Solutions provided.

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Geometry Worksheets with Circle Theorems - Higher GCSE Questions

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  1. Angles – Mixed – With Circle Theorems – 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 clonequestions 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. Edexcel Higher: June 2017 Paper 2, Q15 Edexcel Higher: June 2017 Paper 2, Q15 1 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 GCSE GCSE 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)

  4. Edexcel Higher: November 2017 Paper 3, Q20 Edexcel Higher: November 2017 Paper 3, Q20 1 C 1 C B B GCSE GCSE O O 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. (Total for Question 1 is 4 marks) (Total for Question 1 is 4 marks)

  5. Edexcel Higher : May 2018 Paper 1, Q11 Edexcel Higher : May 2018 Paper 1, Q11 B B 1 1 C C O O GCSE GCSE 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)

  6. Edexcel Higher: June 2018 Paper 2, Q13 Edexcel Higher: June 2018 Paper 2, Q13 1 1 C C O O B B GCSE GCSE E E 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)

  7. Edexcel Higher: November 2017 Paper 1, Q3 Edexcel Higher: November 2017 Paper 1, Q3 < < < < < < < < C 1 D C 1 D 76° 76° < < < < GCSE GCSE B B A A 54° 54° F F E E ABCD is a parallelogram. EAD is a straight line. F is the point on AB so that CFE is a straight line. Angle EFA = 54° Angle ADC = 76° Show that the angle BCF = 50° Give a reason for each stage of your working. ABCD is a parallelogram. EAD is a straight line. F is the point on AB so that CFE is a straight line. Angle EFA = 54° Angle ADC = 76° Show that the angle BCF = 50° Give a reason for each stage of your working. (Total for Question 1 is 4 marks) (Total for Question 1 is 4 marks)

  8. Edexcel Higher: November 2017 Paper 2, Q12 Edexcel Higher: November 2017 Paper 2, Q12 P P 1 1 R R Q Q GCSE GCSE GCSE GCSE RQ and QP are 2 sides of a regular 12-sided polygon. RP is a diagonal of the polygon. Work out the size of angle QPR. You must show your working. RQ and QP are 2 sides of a regular 12-sided polygon. RP is a diagonal of the polygon. Work out the size of angle QPR. You must show your working. (Total for Question 1 is 3 marks) (Total for Question 1 is 3 marks) Edexcel Higher: November 2017 Paper 2, Q12 Edexcel Higher: November 2017 Paper 2, Q12 P P 1 1 R R Q Q RQ and QP are 2 sides of a regular 12-sided polygon. RP is a diagonal of the polygon. Work out the size of angle QPR. You must show your working. RQ and QP are 2 sides of a regular 12-sided polygon. RP is a diagonal of the polygon. Work out the size of angle QPR. You must show your working. (Total for Question 1 is 3 marks) (Total for Question 1 is 3 marks)

  9. Edexcel Higher: June 2017 Paper 3, Q5 Edexcel Higher: June 2017 Paper 3, Q5 1 In the diagram, AB, BC and CD are three sides of a regular polygon K. 1 In the diagram, AB, BC and CD are three sides of a regular polygon K. D D square square polygon K polygon K A A GCSE GCSE C C B B square square Regular 12-sided polygon Regular 12-sided polygon Show that polygon K is a hexagon. You must show your working. Show that polygon K is a hexagon. You must show your working. (Total for Question 1 is 4 marks) (Total for Question 1 is 4 marks)

  10. Edexcel Higher: June 2018 Paper 3, Q8 Edexcel Higher: June 2018 Paper 3, Q8 1 ABCDE is a pentagon. 1 ABCDE is a pentagon. B B 110° 110° A A GCSE GCSE 160° 160° C C E E D D Angle EDC = 2 × angle AED Work out the size of angle EDC You must show all your working. Angle EDC = 2 × angle AED Work out the size of angle EDC You must show all your working. ° ° (Total for Question 1 is 5 marks) (Total for Question 1 is 5 marks)

  11. Edexcel Higher: June 2017 Paper 2, Q15 1 A, B, C and D are four points on the circumference of a circle. C D GCSE 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. Edexcel Higher: November 2017 Paper 3, Q20 1 C B GCSE O 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. (Total for Question 1 is 4 marks)

  13. Edexcel Higher : May 2018 Paper 1, Q11 B 1 C O GCSE 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. Edexcel Higher: June 2018 Paper 2, Q13 1 C O B GCSE E 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. Edexcel Higher: November 2017 Paper 1, Q3 < < < < C 1 D 76° < < GCSE B A 54° F E ABCD is a parallelogram. EAD is a straight line. F is the point on AB so that CFE is a straight line. Angle EFA = 54° Angle ADC = 76° Show that the angle BCF = 50° Give a reason for each stage of your working. (Total for Question 1 is 4 marks)

  16. Edexcel Higher: June 2017 Paper 3, Q5 1 In the diagram, AB, BC and CD are three sides of a regular polygon K. D square polygon K A GCSE C B square Regular 12-sided polygon Show that polygon K is a hexagon. You must show your working. (Total for Question 1 is 4 marks)

  17. Edexcel Higher: June 2018 Paper 3, Q8 1 ABCDE is a pentagon. B 110° A GCSE 160° C E D Angle EDC = 2 × angle AED Work out the size of angle EDC You must show all your working. ° (Total for Question 1 is 5 marks)

  18. 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 GCSE 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)

  19. Edexcel Higher: November 2017 Paper 3, Q20 Edexcel Higher: November 2017 Paper 3, Q20 1 C 1 C a B B b a b y a b x GCSE GCSE 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 = a + a + b + b = 180° < CBO = b = 2a + 2b = 180° < CBA = a + b = a + b = 90° Therefore, angle ABC = 90° Angles on a straight line total 180°. < CBA = = 90° (Total for Question 1 is 4 marks) (Total for Question 1 is 4 marks)

  20. Edexcel Higher : May 2018 Paper 1, Q11 B 1 90° C O GCSE 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 = Base angles in isosceles triangles are equal Angle CBA = + 90 Tangent to a circle is perpendicular to the radius 180 = BAC + 90 + + Angles in a triangle total 180° Rearrange BAC = 90 – 2 (Total for Question 1 is 5 marks)

  21. Edexcel Higher: June 2018 Paper 2, Q13 1 C O B GCSE E 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. Angle CAE = y (alternate segment theorem) Angle EAO = 90 (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)

  22. Edexcel Higher: November 2017 Paper 1, Q3 Edexcel Higher: November 2017 Paper 1, Q3 C 1 D < < < < < < < < C 1 D 76° 76° 50° 50° < < OR < < 76° 54° 76° 54° 104° GCSE GCSE B A B A 54° F 54° F E E ABCD is a parallelogram. EAD is a straight line. F is the point on AB so that CFE is a straight line. Angle EFA = 54° Angle ADC = 76° Show that the angle BCF = 50° Give a reason for each stage of your working. ABCD is a parallelogram. EAD is a straight line. F is the point on AB so that CFE is a straight line. Angle EFA = 54° Angle ADC = 76° Show that the angle BCF = 50° Give a reason for each stage of your working. Angle CFB = 54° Vertically opposite angles are equal. Angle CFB = 54° Vertically opposite angles are equal. Co-Interior angles sum to 180° Angle DAF = 104° Opposite angles in a parallelogram are equal. Angle CBF = 76° Co-Interior angles sum to 180° Angle CBF = 76° Angle BCF = 180 – 76 – 54 = 50° Angle BCF = 180 – 76 – 54 = 50° Angles in a triangle sum to 180 ° Angles in a triangle sum to 180 ° (Total for Question 1 is 4 marks) (Total for Question 1 is 4 marks)

  23. Edexcel Higher: November 2017 Paper 2, Q12 P 1 Total exterior angles = 360° 1 exterior angle = 150° R 30° Q GCSE RQ and QP are 2 sides of a regular 12-sided polygon. RP is a diagonal of the polygon. Work out the size of angle QPR. You must show your working. Interior angle = 180 – 30 = 150° = = 15° 15 (Total for Question 1 is 3 marks)

  24. Edexcel Higher: June 2017 Paper 3, Q5 1 In the diagram, AB, BC and CD are three sides of a regular polygon K. D square polygon K 120° A GCSE 120° C 90° 150° B square Regular 12-sided polygon Show that polygon K is a hexagon. You must show your working. Exterior angle of a 12-sided polygon = 360° ÷ 12 = 30° Interior Angle = 180° – 30° = 150° Angle ABC = 360° - 150° – 90° = 120° Total interior angles of a regular hexagon = (6-2) x 180° = 720° Interior Angle of a regular hexagon = 720° ÷ 6 = 120° Therefore, K is a regular hexagon (Total for Question 1 is 4 marks)

  25. Edexcel Higher: June 2018 Paper 3, Q8 1 ABCDE is a pentagon. B 110° A GCSE 160° C x 60° E 2x 120° D Angle EDC = 2 × angle AED Work out the size of angle EDC You must show all your working. Sum of interior angles of a polygon = = 540 – 160 – 110 – 90 = 180 180 = 3x 60 = x 60 ° (Total for Question 1 is 5 marks)

  26. Questions? Comments? Suggestions? …or have you found a mistake!? Any feedback would be appreciated . Please feel free to email: tom@goteachmaths.co.uk

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