Incenter-Excenter Circle


Given a triangle DeltaA_1A_2A_3, the points A_1, I, and J_1 lie on a line, where I is the incenter and J_1 is the excenter corresponding to A_1. Furthermore, the circle with IJ_1 as the diameter has P as its center, where P is the intersection of A_1J_1 with the circumcircle of DeltaA_1A_2A_3, and passes through A_2 and A_3. This circle has radius


It arises because IJ_1J_2J_3 forms an orthocentric system.

See also

Circumcircle, Excenter, Excenter-Excenter Circle, Incenter, Orthocentric System

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Johnson, R. A. Modern Geometry: An Elementary Treatise on the Geometry of the Triangle and the Circle. Boston, MA: Houghton Mifflin, p. 185, 1929.

Referenced on Wolfram|Alpha

Incenter-Excenter Circle

Cite this as:

Weisstein, Eric W. "Incenter-Excenter Circle." From MathWorld--A Wolfram Web Resource.

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