Orthojoin

The orthojoin of a point is defined as the orthopole of the corresponding trilinear line . In other words, the orthojoin of Kimberling center is equivalent to the orthopole of the line .

It is also the orthopole of the trilinear polar of the isogonal conjugate of .

The following table summarizes the orthojoins of various Kimberling centers.

Kimberling	name	orthojoin	name
	incenter
	triangle centroid
	circumcenter
	orthocenter
	nine-point center
	Gergonne point
	Nagel point
	mittenpunkt
	Spieker center
	first Fermat point
	second Fermat point
	first isodynamic point
	second isodynamic point
	first Napoleon point
	second Napoleon point
	Clawson point