Circle Theorems Mixed Higher GCSE Questions These questions

Circle Theorems – Mixed – 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 clone questions using different numbers. The worksheets are provided in a variety of sizes.

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GCSE 1 Edexcel Higher: June 2017 Paper 2, Q 15 A, B, C and D are four points on the circumference of a circle. C B GCSE 1 Edexcel Higher: June 2017 Paper 2, Q 15 A, B, C and D are four points on the circumference of a circle. C D E B A D E 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)

GCSE 1 Edexcel Higher: November 2017 Paper 3, Q 20 GCSE 1 C Edexcel Higher: November 2017 Paper 3, Q 20 C B B 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. (Total for Question 1 is 4 marks)

GCSE Edexcel Higher : May 2018 Paper 1, Q 11 B 1 C C O 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)

GCSE Edexcel Higher: June 2018 Paper 2, Q 13 1 1 C C O B Edexcel Higher: June 2018 Paper 2, Q 13 O B E E D D A A F F (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)

GCSE 1 Edexcel Higher: June 2017 Paper 2, Q 15 A, B, C and D are four points on the circumference of a circle. C B D E 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)

GCSE 1 Edexcel Higher: November 2017 Paper 3, Q 20 C B 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)

GCSE Edexcel Higher : May 2018 Paper 1, Q 11 B 1 C O 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)

GCSE Edexcel Higher: June 2018 Paper 2, Q 13 1 C O B E D A F (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)

GCSE 1 Edexcel Higher: June 2017 Paper 2, Q 15 A, B, C and D are four points on the circumference of a circle. C X Y D 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. < < BEA = CED Vertically opposite angles are equal. ACD = ABD Angles in the same segment < < BAC = BDC are equal All angles are the same, so the two triangles are similar (Total for Question 1 is 3 marks)

GCSE Edexcel Higher: November 2017 Paper 3, Q 20 1 C b y O b x C B a a a B b 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. < < AOB = x AOC = y Angles at base of isosceles triangle are equal. Angles at the base of an isosceles triangle are equal. < Interior angles of a triangle total 180° a + b + b = 180° < 2 a + 2 b = 180° < a + b = 90° Therefore, angle ABC = 90° Angles on a straight line total 180°. < (Total for Question 1 is 4 marks)

GCSE Edexcel Higher : May 2018 Paper 1, Q 11 B 1 90° C O 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. Rearrange (Total for Question 1 is 5 marks)

GCSE Edexcel Higher: June 2018 Paper 2, Q 13 1 C O B E D A F Angle CAE = y Angle EAO = 90 y = 90 + x y - x = 90 (alternate segment theorem) (tangent to a circle is perpendicular to the radius) (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)

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