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# Tarry Point

The point at which the lines through the polygon 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 equivalent triangle center functions

 (1) (2)

where is the Brocard angle. The Simson line of the Tarry point is perpendicular to the line , when is the circumcenter and is the symmedian point (Lachlan 1893; Johnson 1929; Honsberger 1995, p. 121). The Tarry point of the first Brocard triangle of a triangle is the circumcenter of (Honsberger 1995, pp. 120-121).

Given a triangle with first Neuberg triangle , the lines , , and are concurrent at the Tarry point (Johnson 1929, p. 288).

Brocard Angle, Brocard Triangles, Circumcircle, Symmedian Point, Simson Line, Steiner Points

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## References

Coolidge, J. L. A Treatise on the Geometry of the Circle and Sphere. New York: Chelsea, p. 77, 1971.Gallatly, W. "The Steiner and Tarry Points." §143 in The Modern Geometry of the Triangle, 2nd ed. London: Hodgson, p. 102, 1913.Honsberger, R. "The Steiner Point and the Tarry Point." §10.5 in Episodes in Nineteenth and Twentieth Century Euclidean Geometry. Washington, DC: Math. Assoc. Amer., pp. 119-124, 1995.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.Lachlan, R. An Elementary Treatise on Modern Pure Geometry. London: Macmillian, p. 81, 1893.

Tarry Point

## Cite this as:

Weisstein, Eric W. "Tarry Point." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/TarryPoint.html