Proof of the Circle Theorems

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

A circle with center O. Points A, B, and C are on the circumference. AOC is a diameter, and ABC is an inscribed angle.

Prove that angle $ABC\,$ is $90^\circ\,$

You must not use any circle theorems in your proof.

[4]

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

A circle with center O. Points A, B, and C are on the circumference. AOC is a diameter, and ABC is an inscribed angle.

Prove that angle $ABC\,$ is $90^\circ\,$

You must not use any circle theorems in your proof.

[4]

Proof of the Circle Theorems Questions