Let ,
,
and
be the circles through the vertices and , and , and and , respectively, which intersect
in the first Brocard point . Similarly, define , , and with respect to the second Brocard
point .
Let the two circles and tangent at to and , and passing respectively through and , meet again at , and similarly for and . Then the triangle is called the second Brocard triangle.

The second Brocard triangle is also the triangle obtained as the intersections of the lines ,
,
and
with the Brocard circle, where is the symmedian point.
Let ,
,
and
be the intersections of the lines , , and with the circumcircle
of .
Then ,
,
and
are the midpoints of , , and , respectively (Lachlan 1893).

The following table gives the centers of the second Brocard triangle in terms of the centers of the reference triangle that
correspond to Kimberling centers .