You can move all of the points appearing in the graphic. What do you notice?

What happens to the angle ACB (in black) as C moves around the circle?
What happens to the angle ADB (in red) as D moves along the arc between C and B?
What happens to the line BD as D moves closer to B?
What happens to the exterior angle at B (in blue) as D moves closer to B?
What happens in the limit?
What theorem does this prove?