Creation of this applet was inspired by a [url=https://twitter.com/CutTheKnotMath/status/858332651937312769]tweet[/url] from [url=https://twitter.com/CutTheKnotMath]Alexander Bogomolny[/url].[br][br][b]LARGE points are moveable at any time.[/b] [br][br][b][color=#0000ff]How can you formally prove what this applet informally illustrates? [/color][/b]