Proof of the Circle Theorems

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Hard24%

$B\,$ 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.

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Proof of the Circle Theorems Questions

Practise AQA GCSE Maths Proof of the Circle Theorems with exam-style questions for Foundation and Higher tier. 20 questions, matched to the AQA GCSE Maths (8300) specification and written in Paper 1, Paper 2 and Paper 3 style. Every question includes a full worked solution and mark scheme, so you can see where marks are awarded rather than just whether you got the answer right.