GoGeometry Action 62!

Creation of this applet was inspired by a [url=https://twitter.com/gogeometry/status/871505771636416516]tweet[/url] from [url=https://twitter.com/gogeometry]Antonio Gutierrez[/url]. [br][br]Both circles are tangent to each other at the small white point. [br][br][b][color=#ff00ff]How can we formally prove what this applet informally illustrates? [/color][/b]
Quick (Silent) Demo

Information: GoGeometry Action 62!