In geometry, the circumscribed circle or circumcircle of a polygon is a circle that passes through all the vertices of the polygon. The center of this circle is called the circumcenter and its radius is called the circumradius. Not every polygon has a circumscribed circle. A polygon that does have one is called a cyclic polygon, or sometimes a concyclic polygon because its vertices are concyclic. All triangles, all regular simple polygons, all rectangles, all isosceles trapezoids, and all right kites are cyclic.

Property Value
dbo:abstract
• In geometry, the circumscribed circle or circumcircle of a polygon is a circle that passes through all the vertices of the polygon. The center of this circle is called the circumcenter and its radius is called the circumradius. Not every polygon has a circumscribed circle. A polygon that does have one is called a cyclic polygon, or sometimes a concyclic polygon because its vertices are concyclic. All triangles, all regular simple polygons, all rectangles, all isosceles trapezoids, and all right kites are cyclic. A related notion is the one of a minimum bounding circle, which is the smallest circle that completely contains the polygon within it, if the circle's center is within the polygon. Every polygon has a unique minimum bounding circle, which may be constructed by a linear time algorithm. Even if a polygon has a circumscribed circle, it may be different from its 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. (en)
dbo:thumbnail
dbo:wikiPageID
• 1926432 (xsd:integer)
dbo:wikiPageLength
• 30183 (xsd:integer)
dbo:wikiPageRevisionID
• 983949188 (xsd:integer)
dbp:align
• center (en)
dbp:caption
• The circumcenter of an obtuse triangle is outside the triangle (en)
• The circumcenter of a right triangle is at the midpoint of the hypotenuse (en)
• The circumcenter of an acute triangle is inside the triangle (en)
dbp:image
• Triangle Circumscribed.svg (en)
dbp:title
• Circumcircle (en)
• Cyclic Polygon (en)
• Steiner circumellipse (en)
dbp:totalWidth
• 540 (xsd:integer)
dbp:urlname
• Circumcircle (en)
• CyclicPolygon (en)
• SteinerCircumellipse (en)
dbp:wikiPageUsesTemplate
dct:subject
rdf:type
rdfs:comment
• In geometry, the circumscribed circle or circumcircle of a polygon is a circle that passes through all the vertices of the polygon. The center of this circle is called the circumcenter and its radius is called the circumradius. Not every polygon has a circumscribed circle. A polygon that does have one is called a cyclic polygon, or sometimes a concyclic polygon because its vertices are concyclic. All triangles, all regular simple polygons, all rectangles, all isosceles trapezoids, and all right kites are cyclic. (en)
rdfs:label
• Circumscribed circle (en)
owl:sameAs
prov:wasDerivedFrom
foaf:depiction
foaf:isPrimaryTopicOf
is dbo:wikiPageDisambiguates of
is dbo:wikiPageRedirects of