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

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