Remarks. Suppose all points being considered below lie in a Euclidean plane.
Any two points are concyclic. In fact, there are infinitely many circles that are incident to both and . If , then the pencil of circles incident with and share the property that their centers are collinear. It is easy to see that any point on the perpendicular bisector of serves as the center of a unique circle in .
Any three non-collinear points are concyclic to a unique circle . From the three points, take any two perpendicular bisectors, say of and . Then their intersection is the center of , whose radius is .
Four distinct points are concyclic iff .
|Date of creation||2013-03-22 16:07:58|
|Last modified on||2013-03-22 16:07:58|
|Last modified by||CWoo (3771)|