Ignorance is sad. I'm betting that not A SINGLE ONE OF YOU knows what a cyclic quadrilateral is without googling it. That is terrible. Stop believing in false conspiracies, and learn about the beauty of the universe.
All these are equivalent:
ABCD is cyclic
AD*BC=AB*CD+AD*BC (Ptolemy's, learn the inversion proof because the synthetic one is pretty ugly)
A,B,C,D are concyclic