I can't resist doing it. I don't think I've ever felt like I've contributed something new to the body of knowledge of mathematics before, but I think I might have now. This post modifies an obscure proof I found in a PDF hidden on a long web page (linked in the article) so that it doesn't need trigonometry. The proof is one from triangle geometry (my recent favorite topic), and I haven't found any proof of this fact that's as simple either on the web or in any books. I will happily give credit here if I'm wrong, but I suspect that my proof is among the simplest to follow (for non-triangle-geometry-experts) that exists for the theorem.

Pat, pat, pat.