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The circumscribed circle of a triangle is the unique circle passing through the three vertices (corners).

More generally, if all of the vertices of any polygon lie on a common circle, then that is the polygon's circumscribed circle. Most polygons have no circumscribed circle. Every triangle or rectangle, and every regular polygon, has a circumscribed circle.

The center of the circumscribed circle is the intersection of the perpendicular bisectors of the sides of the triangle.

A cirumscribed circle is not a circumcircle. The circumcircle of an irregular polygon is not the same as the circumscribed circle of the same polygon, as the circumscribed circle intersects each vertex and the circumcircle does not on irregular polygons. However, on a regular polygon the circumcircle and circumscribed circle are the same.

If a triangle, circumscribed in a circle, passes through the center of the circle, that triangle is right.

See also


Elementary geometry

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This article is licensed under the GNU Free Documentation License. It uses material from the "Circumscribed circle".

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