Third circle theorem: 'Angles in the same segment'

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?

If you need it, this theorem is set out here

and all the theorems are summarised here

Tim Devereux, Created with GeoGebra