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).
