Cut-The-Knot-Action 12!

Creation of this applet was inspired by a [url=https://twitter.com/CutTheKnotMath/status/856536986278121472]tweet[/url] from [url=https://twitter.com/CutTheKnotMath]Alexander Bogomolny[/url]. [br][br][b][color=#0000ff]How can you formally prove the phenomena dynamically illustrated here? [/color][/b]
Quick (Silent) Demo

Information: Cut-The-Knot-Action 12!