Proof of the Circle Theorems

$C\,$ and $D\,$ are points on the circumference of a circle, centre $O$ .

A circle with center O. Points A, B, C, and D are on the circumference. Chords AB, AC, BD, and CD are drawn, forming angles ABD and ACD.

Prove that angle $ABD\,$ and angle $ACD\,$ are equal.

[3]

$C\,$ and $D\,$ are points on the circumference of a circle, centre $O$ .

A circle with center O. Points A, B, C, and D are on the circumference. Chords AB, AC, BD, and CD are drawn, forming angles ABD and ACD.

Prove that angle $ABD\,$ and angle $ACD\,$ are equal.

[3]

Proof of the Circle Theorems Questions