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