Carnot Action! = GoGeometry Action 27!

The following applet dynamically illustrates Carnot's Theorem for the case of an OBTUSE TRIANGLE. (The pink slider controls the measure of the obtuse angle with pink vertex.) Without looking it up on another tab in your internet browser, how would you put Carnot's Theorem into words? How can you formally prove what this applet informally illustrates? (A huge thank you to Antonio Gutierrez, whose tweet inspired the creation of this applet.)

Quick (Silent) Demo