Angles in a segment

Author:
T. Gatens
Topic:
Angles, Circle

Dragging the points of these two segments can show that angles in the same segment are equal. But why?

Having labelled, angles A, B & C, what do you know about the relationship between the angles?

You can prove that the angle at the centre of a circle is half the angle at the circumference.

Write a conjecture which summarises this circle theorem.