Equal Areas

I haven't proved this one, yet, but it seems to be true, and it also looks vaguely familiar as something I've seen proved elsewhere. So, if you come up with a proof, or can point me to one, or if you can find a counterexample, let me know:

dave.matthews@mnwest.edu

*** Update: 24/04/09: Michael Tzoumas was smart enough to solve this, and kind enough to e-mail me the solution. I've posted it below the applet. Sorry, the GeoGebra Applet could not be started. Please make sure that Java 1.4.2 (or later) is installed and active in your browser (Click here to install Java now)

Dave Matthews, May 2, 2007, Created with GeoGebra

***** 24/04/09 Here is Michael Tzoumas' solution: