My dynamic geometry sketches Link at
http://math.kennesaw.edu/~mdevilli/JavaGSPLinks.htm has been updated with 'Fermat-Torricelli Point Generalizations' and
'Para-Hexagon Concurrency Theorem', and three new investigations under
the link Student Explorations – one of these generalizes the familiar 'opposite supplementary angles' result of (convex) cyclic quadrilaterals to (convex) cyclic hexagons (and left to the reader to generalize further).