Proof of the Circle Theorems

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Hard

$Y\,$ and $Z\,$ are points on the circumference of a circle, centre $O$ .

A diagram of a circle with center O. Points X, Y, and Z are on the circumference. Radii OX, OY, and OZ are drawn. Angle XOZ is the central angle and angle XYZ is the angle at the circumference.

Prove that angle $XOZ\,$ is double the size of angle $X Y Z$ . You must not use any circle theorems in your proof.

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Proof of the Circle Theorems Questions

Practise Edexcel GCSE Maths Proof of the Circle Theorems with exam-style questions for Foundation and Higher tier. 20 questions, matched to the Edexcel GCSE Maths (1MA1) 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.