A limiting proof of a circle theorem

Topic:
Circle
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?