The isogonal mittenpunkt M' is the isogonal conjugate of the mittenpunkt. It is the homothetic center of the excentral and contact triangles. It has equivalent triangle center functions α_57 | = | 1/(s - a) α_57 | = | 1/(b + c - a) and is Kimberling center X_57. M' lies on the line joining the circumcenter O with the incenter of a triangle Δ A B C, as well as on the line passing through the triangle centroid G, Gergonne point Ge, and mittenpunkt M of Δ A B C.
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