Creation of this applet was inspired (yet again!) by a [url=https://twitter.com/gogeometry/status/816420809560494081]tweet[/url] from [url=https://twitter.com/gogeometry]Antonio Gutierrez[/url]. [br][br]When you see the [color=#9900ff][b]BIG PURPLE POINT APPEAR[/b][/color], feel free to [b][color=#9900ff]place it anywhere along the given side of the triangle on which it's placed[/color][/b]. [br][br][color=#0000ff][i]How can you formally prove what this applet informally illustrates? [/i][/color]