Tucker Hexagon

A Tucker hexagon is a hexagon inscribed in a reference triangle that has sides which are alternately parallel and antiparallel to the corresponding sides of the triangle. Tucker hexagons are always cyclic, and the corresponding circumscribing circle is called a Tucker circle.

Thomsen's figure is similar to a Tucker hexagon; Thomsen's hexagon closes after six parallels, while a Tucker hexagon closes after alternately three parallels and three antiparallels.

See also

Cyclic Polygon, Hexagon, Lemoine Hexagon, Thomsen's Figure, Tucker Circles

This entry contributed by Floor van Lamoen

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Dergiades, N. and Yiu, P. "Antiparallels and Concurrent Euler Lines." Forum Geom. 4, 1-20, 2004., R. Episodes in Nineteenth and Twentieth Century Euclidean Geometry. Washington, DC: Math. Assoc. Amer., pp. 90-91, 1995.van Lamoen, F. M. "Some Concurrencies from Tucker Hexagons." Forum Geom. 2, 5-13, 2002.

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Tucker Hexagon

Cite this as:

van Lamoen, Floor. "Tucker Hexagon." From MathWorld--A Wolfram Web Resource, created by Eric W. Weisstein.

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