Creation of this applet was inspired by a [url=https://twitter.com/CutTheKnotMath/status/781586423610769409]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]Regardless of the locations of points [i][color=#1e84cc][b]N[/b][/color][/i], [i][color=#ff00ff][b]A[/b][/color][/i], and [i][color=#ff00ff][b]B[/b][/color][/i], it will always be true that [math]AP+QB=PQ[/math]. [br][br]How can you formally prove what this applet informally illustrates?