Theorem 19 - Angles in a circle, standing on an arc.
This demonstrates that the angle at the centre of a circle, standing on an arc is twice any angle at the circumference, standing on the same arc.
Drag the point E around the circle to see that the angle at E doesn't change. Drag A or C to change the angle at O. Notice that the angle at E is always half the angle at O. Drag A and C so that the blue arc is longer than the red arc. Notice that the angle at the centre is now reflex.