| __Circumcircle__ *(Site not responding. Last check: 2007-11-07)* |

| | A circle that passes through each of the vertices of a polygon is called the **circumcircle** of the polygon.The center of that circle is the circumcenter.Both seem to be truncations of the prefix “circumscribing” attached to the words circle or center.The word **circumcircle** was suggested in 1883 by W. Hudson in Nature Magazine, according to |

| | Because the circumcenter must be the same distance from each of the vertices, and because each side of the polygon is a chord of the circle, it is easy to understand that the **circumcircle** must be at the intersection of the perpendicular bisectors of the sides of the polygon. |

| | Steiner's theorem, pictured at right, gives a relationship between the radii of five important circles in any triangle, the cirucmcircle, the incircle, and the three excircles (circles tangent to the three sides (or sides extended) of a triangle on the outside of the triangle. |

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