Creation of this applet was inspired by a [url=https://twitter.com/CutTheKnotMath/status/855855860345708544]tweet[/url] from [url=https://twitter.com/CutTheKnotMath]Alexander Bogomolny[/url]. [br][br][b][color=#0000ff]How can you formally prove that the center of the circle that passes through a triangle's incenter and two of its vertices ALSO lies on [/color][color=#9900ff]the bisector of the original triangle's 3rd angle?[/color][/b]