[color=#cc0000][b]Note: [/b][/color][br]Creation of this applet was inspired by a [url=https://twitter.com/CutTheKnotMath/status/791398769459924998]tweet [/url]from [url=https://twitter.com/CutTheKnotMath]Alexander Bogomolny[/url] (at [url=http://www.cut-the-knot.org/]Cut-the-Knot[/url].) [br][br]The applet below dynamically illustrates a theorem known as the [b]Butterfly Theorem[/b]. [br][br]Interact with this applet for a few minutes. As you do, feel free to change the location(s) of any 1 (or more) of the [color=#674ea7][b]BIG POINT(S) that are already there[/b][/color][color=#274e13][b] (or will soon appear)[/b][/color]! [br][br]How can you formally prove what this applet informally illustrates?