Let points 
,
, and 
be marked off some fixed distance 
along each of the sides 
, 
,
and 
. Then the lines 
, 
,
and 
concur in a point 
known as the first Yff point if
 |
(1)
|
This equation has a single real root 
, which can by obtained by solving the cubic
equation
 |
(2)
|
where
 |  |  |
(3)
|
 |  |  |
(4)
|
 |  |  |
(5)
|
The isotomic conjugate 
is called the second Yff point. The triangle
center functions of the first and second points are given by
 |
(6)
|
and
 |
(7)
|
respectively.
Analogous to the inequality 
for the Brocard angle 
, 
holds for the Yff points, with equality in the case of an equilateral
triangle. Analogous to
 |
(8)
|
for 
, 2, 3, the Yff points satisfy
 |
(9)
|
Yff (1963) gives a number of other interesting properties. The line 
is perpendicular to the
line containing the incenter 
and circumcenter 
, and its length is given by
 |
(10)
|
where 
is the area
of the triangle.
The Cevian triangles of the Yff points are known as the Yff triangles.
