defined relative to a reference triangle is called a central line iff is a triangle center (Kimberling 1998, p. 127). If is Kimberling center , then the central line is denoted , and if a central line passes through centers and , the line may be denoted or .
The following table summarizes some named central lines.
central line | prominent incident centers | ||
antiorthic axis | incenter | , , ... | |
Brocard axis | isogonal conjugate of | , , , , , , ... | |
de Longchamps line | third power point | , , ... | |
Euler line | crossdifference of and | , , , , , , , , ... | |
Fermat axis | isogonal conjugate of | , , , , , ... | |
Gergonne line | , , ..., , , ... | ||
Lemoine axis | triangle centroid | , , , , ... | |
line at infinity | symmedian point | , , ... | |
Nagel line | crossdifference of and | , , , , , ... | |
orthic axis | circumcenter | , , , ... | |
Soddy line | crossdifference of and | , , , , , , , ... | |
van Aubel line | isogonal conjugate of | , , , , , ... |
The following pairs of central lines are orthogonal: (Brocard axis, Lemoine axis), (de Longchamps line, Euler line), (Euler line, orthic axis), (Gergonne line, Soddy line).
The following table summarizes the intersections of pairs of lines.