Let three isoscelizers 
, 
, and 
be constructed on a triangle 
, one for each side. This makes
all of the inner triangles similar to each other. However,
there is a unique set of three isoscelizers for which the four interior triangles
,
,
,
and 
are congruent. The innermost triangle 
is called the Yff central triangle (Kimberling
1998, pp. 94-95).
It has trilinear vertex matrix
![[yz z(x+z) y(x+y); z(y+z) zx x(y+x); y(z+y) x(z+x) xy],](/images/equations/YffCentralTriangle/NumberedEquation1.svg) |
where 
,
,
and 
(Kimberling 1998, p. 172; typo corrected).
The original triangle 
is the extangents
triangle of the Yff central triangle 
.
The circumcircle of the Yff central circle is the Yff central circle.
The following table gives the centers of the Yff central triangle in terms of the centers of the reference triangle for Kimberling
centers 
with 
.
 | center of Yff central triangle |  | center of reference triangle |
 | Clawson point |  | congruent isoscelizers point |
 | Bevan point |  | incenter |
 | internal similitude center of circumcircle and incircle |  | Yff center of congruence |
 | orthocenter of the contact triangle |  | first mid-arc point |
