This demonstrates that the angle at the [b]centre[/b] of a circle, standing on an arc is twice any angle [b]at the circumference[/b], standing on the [b]same arc[/b].

Drag the point E around the circle to see that the angle at E doesn't change.[br]Drag A or C to change the angle at O. Notice that the angle at E is always half the angle at O.[br]Drag A and C so that the blue arc is longer than the red arc. Notice that the angle at the centre is now [b]reflex.[/b]