The angle at the centre is twice the angle at the cirmfrnc

Topic:
Angles
Use the applet to verify the theorem stating that "The angle subtended by an arc at the centre of a circle is double the size of the angle subtended by the same arc at the circle circumference (on the same side of the arc/chord as the centre)". You can vary the angle by moving either point B or D.
What is the relationship between the angle at center circle and angle at circumference? I think we now we have a conjecture, which we could express as the angle at the centre is twice the angle at the circumference. Can you prove it?