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.