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Orthocorrespondent

The trilinear pole of the orthotransversal of a point is called its orthocorrespondent.

The orthocorrespondent of a point is given by

where , , and is Conway triangle notation.

In general, there are two (not necessarily real) points sharing the same orthocorrespondent. These points are inverse in the polar circle. However, all points at infinity have the triangle centroid as their orthocorrespondent.

The following table gives the orthocorrespondents of finite Kimberling centers whose orthocorrespondents are also Kimberling centers.

 center orthocorrespondent incenter isogonal conjugate of triangle centroid orthocorrespondent of circumcenter orthocorrespondent of nine-point center orthocorrespondent of symmedian point orthocorrespondent of Gergonne point orthocorrespondent of Nagel point orthocorrespondent of mittenpunkt orthocorrespondent of Spieker center orthocorrespondent of Feuerbach point trilinear pole of line first Fermat point first Fermat point second Fermat point second Fermat point first isodynamic point isogonal conjugate of second isodynamic point isogonal conjugate of Clawson point orthocorrespondent of third power point orthocorrespondent of perspector of the orthic and intangents triangles orthocorrespondent of inverse-in-circumcircle of incenter orthocorrespondent of isogonal conjugate of orthocorrespondent of isogonal conjugate of orthocorrespondent of reflection of incenter in Feuerbach point orthocorrespondent of Tarry point -Hirst inverse of anticomplement of Feuerbach point orthocorrespondent of psi(incenter, symmedian point) orthocorrespondent of antipode of inverse Mimosa transform of lambda(incenter, symmedian point) inverse Mimosa transform of lambda(incenter, triangle centroid) inverse Mimosa transform of psi(symmedian point, orthocenter) trilinear pole of Euler line psi(circumcenter, orthocenter) trilinear pole of line psi(incenter, circumcenter) inverse Mimosa transform of Parry point isogonal conjugate of psi(orthocenter, symmedian point) focus of Kiepert parabola Jerabek antipode Dc() Kiepert antipode Dc() Kiepert center focus of Kiepert parabola midpoint of and Dc() midpoint of and Dc() Feuerbach antipode Dc() -of-medial triangle Dc() Jerabek center trilinear pole of Euler line -of-orthic triangle -Hirst inverse of inverse-in-circumcircle of orthocorrespondent of -line conjugate of orthocorrespondent of of the orthic triangle orthocorrespondent of -line conjugate of orthocorrespondent of isogonal conjugate of Dc() -cross conjugate of Dc() Collings transform of Dc() orthojoin of isogonal conjugate of orthojoin of trilinear pole of line Mimosa transform of isogonal conjugate of Zosma transform of orthocorrespondent of Zosma transform of orthocorrespondent of

Orthotransversal

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References

Gibert, B. "Orthocorrespondence and Orthopivotal Cubics." Forum Geom. 3, 1-27, 2003a. http://forumgeom.fau.edu/FG2003volume3/FG200301index.html.Gibert, B. "Antiorthocorrespondents of Circumconics." Forum Geom. 3, 231-249, 2003b. http://forumgeom.fau.edu/FG2003volume3/FG200326index.html.Gibert B. "Orthopivotal Cubics." http://perso.wanadoo.fr/bernard.gibert/gloss/orthopivotalcubi.html.Gibert, B. and van Lamoen, F. M. "The Parasix Configuration and Orthocorrespondence." Forum Geom. 3, 169-180, 2003. http://forumgeom.fau.edu/FG2003volume3/FG200318index.html.

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Orthocorrespondent

Cite this as:

Weisstein, Eric W. "Orthocorrespondent." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Orthocorrespondent.html