A Brocard line is a line from any of the vertices 
of a triangle 
to the first 
or second 
Brocard
point. Let the angle at a vertex 
also be denoted 
, and denote the intersections of 
and 
with 
as 
and 
. Then the angles involving these
points are
 |  |  |
(1)
|
 |  |  |
(2)
|
 |  |  |
(3)
|
Distances involving the point 
satisfy
 |
(4)
|
where 
is the Brocard angle (Johnson 1929, pp. 267-268).
If 
is the triangle
centroid and 
is the symmedian point of a triangle 
, then the lines 
, 
, and 
meet at a point 
. Similarly, 
, 
, and 
meet at a point 
which is the isogonal
conjugate point of 
(Johnson 1929, pp. 268-269).
