The orthic inconic of a triangle is the inconic with inconic parameters
 |
(1)
|
It has trilinear equation
 |
(2)
|
(P. Moses, pers. comm., Feb. 8, 2005), where 
, 
, and 
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
 |
(3)
|
where 
is the area of the reference
triangle.
It has the orthocenter 
as its Brianchon point
and the symmedian point 
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 
for 
(the center of the Jerabek
hyperbola) and 2969.
The axes of the orthic inconic are parallel to the asymptotes of the Jerabek hyperbola.
