Proof of the Circle Theorems

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Question 13

$Y\,$ 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.

[4]

Proof of the Circle Theorems

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

Question 13

$Y\,$ 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.

[4]

Proof of the Circle Theorems

Question 13

Markscheme

Proof of the Circle Theorems

Question 13

Markscheme

Proof of the Circle Theorems

Question 13

Proof of the Circle Theorems Questions

Proof of the Circle Theorems

Question 13

Proof of the Circle Theorems Questions