Proof of the Circle Theorems

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

A circle with centre O and points X, Y and Z on its circumference, with radii and chords shown.

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

[4]

Proof of the Circle Theorems

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

A circle with centre O and points X, Y and Z on its circumference, with radii and chords shown.

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

[4]

Proof of the Circle Theorems

Proof of the Circle Theorems Questions