Cyclic Quadrilateral

Points which lie on a circle are called concyclic points.

Given one or two points there are infinitely many circles passing through them.
Three non-collinear points are always concyclic and there is only one circle passing through all of them.
Three collinear points are not concyclic (or noncyclic).
Four non-collinear points may or may not be concyclic.

A quadrilateral is said to be a cyclic quadrilateral if there is a circle passing through all its four vertices.

Sum of the opposite angles of a cyclic quadrilateral is 180°.