Miquel Theorems

Let us consider a system of n elements x₁, x₂,........, x_n in a plane which may be of any of the following types :-

(i) It may consist of n straight lines intersecting in pairs in distinct points of intersection.

(ii) It may consist of n circles intersecting in a point O and having their other intersections all distinct.

(iii) It may consist of n - 1 circles and a straight line intersecting in a common point O and having their other intersections all distinct.