Cut-The-Knot Action (2) !!!

Topic:
Circle
Creation of this applet was inspired by a tweet from Alexander Bogomolny (Cut-The-Knot.org). Slide the slider very slowly and carefully observe the dynamics taking place. Feel free to move the BIG WHITE POINTS anywhere you'd like at any time! How can you formally prove what this applet informally illustrates?

Quick (Silent) Demo