A,B A, B\,A,B and C C\,C are points on the circumference of a circle, centre OOO. AOC AOC\,AOC is a diameter of the circle.

Prove that angle ABC ABC\,ABC is 90∘ 90^\circ\,90∘
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.