Cyclic Quadrilateral

Concyclic Points

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.

Cyclic Quadrilateral

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°.