I did hear you but I wasn't talking to you, I was addressing the question posed by the original poster.

It's nice to see that you posted your little theorem; for the purposes of checking it, could I ask if you are referring to the bisector of the opposite sides, or the bisector of the angle?

You should know that all of this stuff although pretty is rather antiquated; it's easy to discover and to prove (or disprove) such theorems nowadays using more modern vector methods, and there's not really much use for them.