Steiner point (triangle)

In triangle geometry, the Steiner point is a particular point associated with a plane triangle. It is a triangle center and it is designated as the center X(99) in Clark Kimberling's Encyclopedia of Triangle Centers. Jakob Steiner (1796–1863), Swiss mathematician, described this point in 1826. The point was given Steiner's name by Joseph Neuberg in 1886.

The Steiner point is defined as follows. (This is not the way in which Steiner defined it.)

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. Let ABC be any given 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. The Tarry point is a triangle center and it is designated as the center X(98) in Encyclopedia of Triangle Centers. The trilinear coordinates of the Tarry point are given below:

Similar to the definition of the Steiner point, the Tarry point can be defined as follows:

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