The Steiner point of a triangle ABC is
constructed as follows: First, let O be the
and K the symmedian (or
Lemoine) point of ABC. The circle having segment OK as
diameter is the Brocard circle. The line through O perpendicular
to line BC passes through the Brocard circle in another point,
A'; similarly, obtain points B' and C'. The triangle A'B'C' is
the Brocard triangle. Now, construct the line through A
parallel to line B'C', the line through B parallel to line C'A',
and the line through C parallel to line A'B'. These three lines
concur in the Steiner point, S. It lies on the circumcircle.
The point was studied by Jakob Steiner
(1796-1863) Swiss mathematician.