Isogonal Mittenpunkt

The isogonal mittenpunkt M^' is the isogonal conjugate of the mittenpunkt. It is the homothetic center of the excentral and contact triangles (Gallatly 1913, pp. 17-18). It has equivalent triangle center functions


and is Kimberling center X_(57) (Kimberling 1998, p. 75).


M^' lies on the line joining the circumcenter O with the incenter of a triangle DeltaABC (Gallatly 1913, pp. 17-18), as well as on the line passing through the triangle centroid G, Gergonne point Ge, and mittenpunkt M of DeltaABC (Gallatly 1913, p. 22).

See also

Isogonal Conjugate, Mittenpunkt

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Gallatly, W. The Modern Geometry of the Triangle, 2nd ed. London: Hodgson, 1913.Kimberling, C. "Triangle Centers and Central Triangles." Congr. Numer. 129, 1-295, 1998.Kimberling, C. "Encyclopedia of Triangle Centers: X(57)=Isogonal Conjugate of X(9)."

Referenced on Wolfram|Alpha

Isogonal Mittenpunkt

Cite this as:

Weisstein, Eric W. "Isogonal Mittenpunkt." From MathWorld--A Wolfram Web Resource.

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