Circle Properties Theorem 19
Theorem 19. The angle at the centre of a circle standing on a given arc is twice the angle at any point of the circle standing on the same arc.
Proof. There are several cases for the diagram. It will be sufficient for stu-
dents to examine one of these. The idea, in all cases, is to draw the line
through the centre and the point on the circumference, and use the Isosce-
les Triangle Theorem, and then the Protractor Axiom (to add or subtract
angles, as the case may be).
