Proof of the Circle Theorems

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Question 1

30%

$B\,$ and $C\,$ are points on the circumference of a circle, centre $O$ .

A diagram of a circle with center O. Points A, B, and C are on the circumference. Line segments OB, OA, and OC are drawn from the center to the points. Angle AOC is the central angle, and angle ABC is the inscribed angle subtending the same arc AC.

Prove that angle $AOC\,$ is twice the size of angle $A B C$ . You must not use any circle theorems in your proof.

[4]

Proof of the Circle Theorems

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Question 1

30%

$B\,$ and $C\,$ are points on the circumference of a circle, centre $O$ .

A diagram of a circle with center O. Points A, B, and C are on the circumference. Line segments OB, OA, and OC are drawn from the center to the points. Angle AOC is the central angle, and angle ABC is the inscribed angle subtending the same arc AC.

Prove that angle $AOC\,$ is twice the size of angle $A B C$ . You must not use any circle theorems in your proof.

[4]

Proof of the Circle Theorems

Question 1

Markscheme

Proof of the Circle Theorems

Question 1

Markscheme

Proof of the Circle Theorems

Question 1

Proof of the Circle Theorems Questions

Proof of the Circle Theorems

Question 1

Proof of the Circle Theorems Questions