The center of a Triangle's Circumcircle. It can be found as the intersection of the Perpendicular Bisectors. If the Triangle is Acute, the circumcenter is in the interior of the Triangle. In a Right Triangle, the circumcenter is the Midpoint of the Hypotenuse.

(1) |

(2) |

(3) |

(4) |

The circumcenter and Orthocenter are Isogonal Conjugates.

The Orthocenter of the Pedal Triangle formed by the Circumcenter concurs with the circumcenter itself, as illustrated above. The circumcenter also lies on the Euler Line.

**References**

Carr, G. S. *Formulas and Theorems in Pure Mathematics, 2nd ed.* New York: Chelsea, p. 623, 1970.

Dixon, R. *Mathographics.* New York: Dover, p. 55, 1991.

Eppstein, D. ``Circumcenters of Triangles.'' http://www.ics.uci.edu/~eppstein/junkyard/circumcenter.html.

Johnson, R. A. *Modern Geometry: An Elementary Treatise on the Geometry of the Triangle and the Circle.* Boston, MA:
Houghton Mifflin, 1929.

Kimberling, C. ``Central Points and Central Lines in the Plane of a Triangle.'' *Math. Mag.* **67**, 163-187, 1994.

Kimberling, C. ``Circumcenter.'' http://cedar.evansville.edu/~ck6/tcenters/class/ccenter.html.

© 1996-9

1999-05-26