X,Y X, Y\,X,Y and Z Z\,Z are points on the circumference of a circle, centre OOO.

Prove that angle XOZ XOZ\,XOZ is double the size of angle XYZXYZXYZ. You must not use any circle theorems in your proof.
Practise Eduqas GCSE Maths Proof of the Circle Theorems with exam-style questions for Foundation and Higher tier. 20 questions, matched to the Eduqas GCSE Maths (C300QS) specification and written in Component 1 and Component 2 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.