Difference between revisions of "Circumcircle"
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The '''circumcircle''' of a [[triangle]] or other [[polygon]] is the [[circle]] which passes through all of its [[vertex|vertices]]. Every triangle has a circumcircle, but most other polygons do not. For instance, those [[quadrilateral]]s with circumcircles form a special class, known as [[cyclic quadrilateral]]s. | The '''circumcircle''' of a [[triangle]] or other [[polygon]] is the [[circle]] which passes through all of its [[vertex|vertices]]. Every triangle has a circumcircle, but most other polygons do not. For instance, those [[quadrilateral]]s with circumcircles form a special class, known as [[cyclic quadrilateral]]s. | ||
Revision as of 18:59, 9 October 2008
| This is an AoPSWiki Word of the Week for October 10-October 16 |
The circumcircle of a triangle or other polygon is the circle which passes through all of its vertices. Every triangle has a circumcircle, but most other polygons do not. For instance, those quadrilaterals with circumcircles form a special class, known as cyclic quadrilaterals.
The center of the circumcircle is known as the circumcenter. It is the intersection of the perpendicular bisectors of the edges of the polygon.
The radius of the circumcirle is known as the circumradius. For triangles, the circumradius appears in a number of significant roles, such as in the Law of Sines.
