Tarry Point


The point T 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 S. It has equivalent triangle center functions


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 symmedian point (Lachlan 1893; Johnson 1929; Honsberger 1995, p. 121). The Tarry point of the first Brocard triangle of a triangle DeltaABC is the circumcenter of DeltaABC (Honsberger 1995, pp. 120-121).


Given a triangle DeltaA_1A_2A_3 with first Neuberg triangle DeltaN_1N_2N_3, the lines A_1N_1, A_2N_2, and A_3N_3 are concurrent at the Tarry point T (Johnson 1929, p. 288).

See also

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

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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.

Referenced on Wolfram|Alpha

Tarry Point

Cite this as:

Weisstein, Eric W. "Tarry Point." From MathWorld--A Wolfram Web Resource.

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