The first Brocard point 
is the interior point 
(also denoted 
or 
) of a triangle 
with points labeled in counterclockwise order
for which the angles 
, 
, and 
are equal, with the unique such angle denoted 
and called the Brocard
angle. The first Brocard point 
fails to be a triangle
center because it is bicentric with the second Brocard point 
, but it has trilinear
coordinates
 |
(1)
|
(Kimberling 1998, p. 47).
Note that extreme care is needed when consulting the literature, since reversing the order in which the points of the triangle are labeled results in exchanging the Brocard points.
Distances involving the second Brocard point include
 |  |  |
(2)
|
 |  |  |
(3)
|
 |  |  |
(4)
|
 |  |  |
(5)
|
(Johnson 1929, pp. 267-268), where 
is the Brocard angle.
, 
du plan d'un triangle 
qui se déduisent d'un point 
quelconque di plan comme les points de Brocard de déduisent
du point de Lemoine." Mathesis 6, Suppl. 3, 1-22, 1886.