Creation of this applet was inspired by a [url=https://twitter.com/gogeometry/status/851134461945270272]tweet[/url] from [url=https://twitter.com/gogeometry]Antonio Gutierrez[/url]. [br][br]White points are moveable at any time. [br][br][b][color=#0000ff]How can you formally prove what this applet informally illustrates?[/color][/b]