Incircle + Excircle = GoGeometry Action 31!

Creation of this applet was inspired by a [url=https://twitter.com/gogeometry/status/855427001963958272]tweet[/url] from [url=https://twitter.com/gogeometry]Antonio Gutierrez[/url]. [br][br][b][color=#0000ff]How can you formally prove the phenomena dynamically illustrated here? [/color][/b]
Quick (Silent) Demo

Information: Incircle + Excircle = GoGeometry Action 31!