Creation of this applet was inspired by a [url=https://twitter.com/CutTheKnotMath/status/803271102973755392]tweet[/url] from [url=https://twitter.com/CutTheKnotMath]Alexander Bogomolny[/url] ([url=http://www.cut-the-knot.org/]Cut-The-Knot.org[/url]). [br][br][b]Slide the slider very slowly and carefully observe the dynamics taking place. [/b][br][i]Feel free to move the BIG WHITE POINTS anywhere you'd like at any time! [/i][br][br]How can you formally prove what this applet informally illustrates?