Mickey Mouse Theorem! (Cut-the-Knot Action 16)

Angles, Circle
Creation of this applet was inspired by a tweet from Alexander Bogomolny. Each gray circle is tangent to the tan-colored circle. Feel free to move the BIG WHITE POINTS and/or BIG GRAY POINTS anywhere you'd like. How would you describe the phenomena you see in words? How can we formally prove what is informally illustrated here?

Quick (Silent) Demo