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B 3 B
1 C
O
O
C D
A
A
A, B, C and D are points on the circumference of a circle, centre O.
A, B and C are points on the circumference of a circle, centre O.
Prove that angle ABD and angle ACD are equal.
Prove that angle AOC is twice the size of angle ABC.
You must not use any circle theorems in your proof. (2 marks)
(4 marks)
4
B
B C
2
A
O
O
C A
D
A, B and C are points on the circumference of a circle, centre O. A, B, C and D are points on the circumference of a circle, centre O.
AOC is a diameter of the circle. Prove that angle ABC and angle ADC add to 180°
Prove that angle ABC is 90° (4 marks)
You must not use any circle theorems in your proof.
(4 marks)
Grade 9 Proof of the Circle Theorems Grade 9
B 3 B
1 C
O
O
C D
A
A
A, B, C and D are points on the circumference of a circle, centre O.
A, B and C are points on the circumference of a circle, centre O.
Prove that angle ABD and angle ACD are equal.
Prove that angle AOC is twice the size of angle ABC.
You must not use any circle theorems in your proof. (2 marks)
(4 marks)
4
B
B C
2
A
O
O
C A
D
A, B and C are points on the circumference of a circle, centre O. A, B, C and D are points on the circumference of a circle, centre O.
AOC is a diameter of the circle. Prove that angle ABC and angle ADC add to 180°
Prove that angle ABC is 90° (4 marks)
You must not use any circle theorems in your proof.
(4 marks)
Grade 9 Proof of the Circle Theorems Grade 9
