Circumcircle

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The circumcircle of a triangle or other polygon is the circle which passes through all of its vertices (if such a circle exists). Every triangle has one (and only one) circumcircle, but most other polygons do not. Regular polygons do have circumcircles. 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 circumcircle is known as the circumradius. For triangles, the circumradius appears in a number of significant roles, such as in the Law of Sines.

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