Editing Concyclic points (section)

== Minimum bounding circle ==

A related notion is the one of a [[Smallest circle problem|minimum bounding circle]], which is the smallest circle that completely contains a set of points. Every set of points in the plane has a unique minimum bounding circle, which may be constructed by a [[linear time]] algorithm.<ref>{{cite journal|first=N.|last=Megiddo|title=Linear-time algorithms for linear programming in '''R'''{{sup|3}} and related problems|journal=SIAM Journal on Computing|volume=12|issue=4|pages=759–776|year=1983|doi=10.1137/0212052|s2cid=14467740}}</ref>

Even if a set of points are concyclic, their circumscribing circle may be different from their minimum bounding circle. For example, for an [[obtuse triangle]], the minimum bounding circle has the longest side as diameter and does not pass through the opposite vertex.