homology center | perspective pole

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 Δ A B C, the perspector of Δ A B C 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 Δ A B C 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.

perspective center | perspective triangles | perspectrix