Third circle theorem

First page
Theorem 1
Theorem 2
Theorem 3
Theorem 4
Theorem 5
Theorem 6
Theorem 7
The Seven Theorems

Angles in the same segment

Third circle theorem:

Compare the sizes of angles α & β, as you use the cursor to move point C or D around the circumference.
It doesn't change either angle β- they stay the same!
What is the effect of moving point E?
And finally, what happens when you move point B?

This is a Java Applet created using GeoGebra from - it looks like you don't have Java installed, please go to

If you need them, the seven circle theorems here

Tim Devereux, Created with GeoGebra