The point at which the three lines connecting the vertices of two perspective triangles concur, sometimes also called the perspective center, homology center, or pole.
In the plane of a reference triangle , the perspector of and its polar triangle with respect to a given conic is called the perspector of that conic. The perspector is not defined for conics with respect to which is self-polar. For an inconic, the perspector is the Brianchon point of the conic.
The following table summarizes perspectors of some named triangle conics corresponding to Kimberling centers.
conic | Kimberling | perspector |
anticomplementary triangle | orthocenter | |
Bevan circle | isogonal conjugate of | |
Brocard inellipse | symmedian point | |
circumcircle | symmedian point | |
de Longchamps circle | -cross conjugate of | |
excircles radical circle | exsimilicenter(nine-point circle, Apollonius circle) | |
Feuerbach hyperbola | crossdifference of and | |
first Droz-Farny circle | orthocenter | |
incircle | Gergonne point | |
Jerabek hyperbola | crossdifference of and | |
Kiepert hyperbola | isogonal conjugate of | |
Kiepert parabola | Steiner point | |
Lemoine inellipse | isogonal conjugate of | |
MacBeath circumconic | circumcenter | |
MacBeath inconic | isotomic conjugate of the circumcenter | |
Mandart inellipse | Nagel point | |
orthic inconic | orthocenter | |
Spieker circle | triangle centroid | |
Steiner circumellipse | triangle centroid | |
Steiner inellipse | triangle centroid | |
tangential circle | ||
tangential mid-arc circle | third mid-arc point | |
Yff parabola | Yff parabolic point |
The following table lists the perspectors of pairs of special triangles.