Creation of this applet was inspired by a [url=https://twitter.com/CutTheKnotMath/status/964231592372834305]tweet[/url] from [url=https://twitter.com/CutTheKnotMath]Alexander Bogomolny[/url]. [br][br]You can move the [b]VERTICES[/b] of the triangle anywhere you'd like at any time. [br][color=#ff00ff][b]You can also change the size of the pink angle by using the pink slider. [/b][/color][br][color=#1e84cc]You can move the [b]LARGE TURQUOISE POINT[/b] (soon-to-appear) as well. [br][/color][br][b]How can we formally prove what is dynamically illustrated here? [/b]