Orthic Inconic

The orthic inconic of a triangle is the inconic with inconic parameters


It has trilinear equation


(P. Moses, pers. comm., Feb. 8, 2005), where S_A, S_B, and S_C are Conway triangle notation.


It is an ellipse for acute triangles and a hyperbola for obtuse triangles.

When the orthic inconic is an inellipse, it has area


where Delta is the area of the reference triangle.

It has the orthocenter H as its Brianchon point and the symmedian point K as its center. Its contact points with the reference triangle form the orthic triangle, which is also its polar triangle.

The orthic inconic passes through Kimberling centers X_i for i=125 (the center of the Jerabek hyperbola) and 2969.

The axes of the orthic inconic are parallel to the asymptotes of the Jerabek hyperbola.

See also

Brianchon Point, Inconic, Inellipse, MacBeath Circumconic, Orthic Triangle

Explore with Wolfram|Alpha


Parry, C. F. "The Isogonal Tripolar Conic." Forum Geom. 1, 33-42, 2001.

Referenced on Wolfram|Alpha

Orthic Inconic

Cite this as:

Weisstein, Eric W. "Orthic Inconic." From MathWorld--A Wolfram Web Resource.

Subject classifications