Tarry Point

The point at which the lines through the Vertices of a Triangle Perpendicular to the corresponding sides of the first Brocard Triangle, are Concurrent. The Tarry point lies on the Circumcircle opposite the Steiner Point. It has Triangle Center Function

$$\alpha={bc\over b^4+c^4-a^2b^2-a^2c^2} = \sec(A+\omega),$$

where $\omega$ is the Brocard Angle. The Simson Line of the Tarry point is Perpendicular to the line $OK$, when $O$ is the Circumcenter and $K$ is the Lemoine Point.

See also Brocard Angle, Brocard Triangles, Circumcircle, Lemoine Point, Simson Line, Steiner Points

References

Gallatly, W. The Modern Geometry of the Triangle, 2nd ed. London: Hodgson, p. 102, 1913.

Johnson, R. A. Modern Geometry: An Elementary Treatise on the Geometry of the Triangle and the Circle. Boston, MA: Houghton Mifflin, pp. 281-282, 1929.

Kimberling, C. ``Central Points and Central Lines in the Plane of a Triangle.'' Math. Mag. 67, 163-187, 1994.