Editing Concyclic points (section)

{{Short description|Points on a common circle}}
{{Also|Circumgon}}
[[File:Concyclic.svg|thumb|[[Concurrent lines|Concurrent]] perpendicular bisectors of [[Circle#Chord|chords]] between concyclic points]]
[[File:Circumscribed Polygon.svg|thumb|Circumscribed circle, {{mvar|C}}, and circumcenter, {{mvar|O}}, of a ''cyclic polygon'', {{mvar|P}}]]

In [[geometry]], a [[set (mathematics)|set]] of [[point (geometry)|points]] are said to be '''concyclic''' (or '''cocyclic''') if they lie on a common [[circle]]. A [[polygon]] whose [[vertex (geometry)|vertices]] are concyclic is called a '''cyclic polygon''', and the circle is called its ''circumscribing circle'' or ''circumcircle''. All concyclic points are [[equidistant]] from the center of the circle.

Three points in the [[Euclidean plane|plane]] that do not all fall on a [[straight line]] are concyclic, so every [[triangle]] is a cyclic polygon, with a well-defined [[circumcircle]]. However, four or more points in the plane are not necessarily concyclic. After triangles, the special case of [[cyclic quadrilateral]]s has been most extensively studied.