Creation of this applet was inspired by a [url=https://twitter.com/gogeometry/status/892023508812910592]tweet[/url] from [url=https://twitter.com/gogeometry]Antonio Gutierrez[/url] (GoGeometry).[br][br][b]Feel free to move the LARGE BLACK POINTS anywhere along the circle at any time. [br][/b][br][b][color=#9900ff]How can we formally prove what this applet informally illustrates? [br][/color][/b][br]