Difference between revisions of "Circumcircle"
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{{WotWAnnounce|week=October 10-October 16}} | {{WotWAnnounce|week=October 10-October 16}} | ||
| − | The '''circumcircle''' of a [[triangle]] or other [[polygon]] is the [[circle]] which passes through all of its [[vertex|vertices]]. Every triangle has | + | The '''circumcircle''' of a [[triangle]] or other [[polygon]] is the [[circle]] which passes through all of its [[vertex|vertices]]. Every triangle has one (and only one) circumcircle, but most other polygons do not. For instance, those [[quadrilateral]]s with circumcircles form a special class, known as [[cyclic quadrilateral]]s. |
| − | The center of the circumcircle is known as the [[circumcenter]]. It is the [[intersection]] of the [[perpendicular bisector]]s of the [[ | + | The center of the circumcircle is known as the [[circumcenter]]. It is the [[intersection]] of the [[perpendicular bisector]]s of the [[side]]s of the polygon. |
| − | The radius of the | + | The radius of the circumcircle is known as the [[circumradius]]. For triangles, the circumradius appears in a number of significant roles, such as in the [[Law of Sines]]. |
[[Image:Circumcircle2.PNG|center]] | [[Image:Circumcircle2.PNG|center]] | ||
Revision as of 17:02, 10 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 one (and only one) 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 sides of the polygon.
The radius of the circumcircle is known as the circumradius. For triangles, the circumradius appears in a number of significant roles, such as in the Law of Sines.
