That generalization is really pretty, I hadn't thought of that. It can be proved by letting points come together in Pascals hexagon theorem, is that how you did it? Also, if you wouldn't mind I would be interested to see how you proved(a sketch would be enough) the second problem I posted. My proof gets kinda heavy into trig, but I've always preferred proofs that don't use trig, so I'd be curious to see how you do it.

Greg