The Yff contact triangle 
(a term coined here for the first time), is the
Cevian triangle of Kimberling center 
.
It is the polar triangle of the Yff parabola.
It has the trilinear vertex matrix
![[0 (ac)/(c-a) (ab)/(b-a); (bc)/(b-c) 0 (ab)/(a-b); (bc)/(b-c) (ac)/(c-a) 0].](/images/equations/YffContactTriangle/NumberedEquation1.svg) |
(1)
|
The vertices are the points of contact of the Yff parabola with the sidelines of the reference triangle.
Since it is the Cevian triangle of a point on the Steiner circumellipse, it has area
 |
(2)
|
where 
is the area of the reference triangle and the
negative sign indicates that the orientation is reversed.
The circumcircle of the Yff contact triangle is the Yff contact circle.
The triangle centroid of 
has triangle center function
 |
(3)
|
and lies on the lines (2,514), (63,649), (210,513), (514,1022), (612,1027), (661,1211) (P. Moses, pers. comm., Jan. 18, 2005).
Its orthocenter is the Nagel point 
(P. Moses, pers. comm., Jan. 18, 2005).
