GoGeometry Action 70!

Creation of this applet was inspired by a [url=https://twitter.com/gogeometry/status/878994669790777344]tweet[/url] from [url=https://twitter.com/gogeometry]Antonio Gutierrez[/url] (GoGeometry.) [br][br]Shown in this diagram are 2 circles, a common internal tangent, and a common external tangent. [br][b][color=#38761d]You can adjust the size of the green circle by using the green slider. [/color][/b] [br][color=#ff00ff][b][br]How can we formally prove what this applet informally illustrates? [/b][/color]

Information: GoGeometry Action 70!