Steiner point (triangle)

Jakob Steiner (1796–1863), Swiss mathematician, described this point in 1826.

The point was given Steiner's name by Joseph Neuberg in 1886.

[2]) In the Encyclopedia of Triangle Centers the Steiner point is defined as follows; The trilinear coordinates of the Steiner point are given below.

The Tarry point of a triangle is closely related to the Steiner point of the triangle.

The point on the circumcircle of triangle ABC diametrically opposite to the Steiner point of triangle ABC is called the Tarry point of triangle ABC.

Construction of the Steiner point.
Triangle ABC
Triangle A'B'C' ( Brocard triangle of ABC )
Circumcircle of triangle ABC , centered at O
Brocard circle of triangle ABC

Lines concurring at the Steiner point:
L A : line through A parallel to B'C'
L B : line through B parallel to C'A'
L C : line through C parallel to A'B'
Alternative construction of the Steiner point
The line through A perpendicular to B'C' , the line through B perpendicular to C'A' , and the line through C perpendicular to A'B' concur at the Tarry point.