Unproved Conjectures

The problems below are either problems that I've not yet managed to solve or ones that I've not had much time to work on. It is hoped that by sharing them here, others may become interested in solving some of these.

Cyclic Quadrilateral Conjecture

Nested Fermat Quadrilaterals Conjecture

Prove that the results at Parallelo-hexagon Areas are also true for crossed parallelo-hexagons.

Sandor Szanto's Conjectures with respect to my generalization of Neuberg's theorem and the Miquel line

***

If anyone visiting here manages to prove or refute any of the conjectures above, please let me know so as to update its status. It may also be that they are not original and already appear in some journal or book somewhere - such references would be appreciated.

Updated, Michael de Villiers, 16 July 2011.