de Longchamps Line


The de Longchamps line is central line L_(32) with trilinear equation


(Droussent 1953; Kimberling 1998, p. 150) which is the anticomplement of the orthic axis L_1 (correcting the typo of Kimberling 1998, p. 150).

It is perpendicular to the Euler line at Kimberling center X_(858).

It passes through Kimberling centers X_i for i=325, 523, 684, 693, 850, 858, 1273, 1491, 2512, 2513, 2514, 2517, 3001, 3004, 3005, 3006, 3007, and 3014.


The de Longchamps line is the radical line of the coaxal system consisting of (anticomplementary circle, circumcircle, de Longchamps circle)

See also

Antiorthic Axis, Coaxal System

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Droussent, L. "Cubiques circulaires anallagmatiques par points réciproques on isogonaux." Mathesis 62, 204-215, 1953.Kimberling, C. "Triangle Centers and Central Triangles." Congr. Numer. 129, 1-295, 1998.

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de Longchamps Line

Cite this as:

Weisstein, Eric W. "de Longchamps Line." From MathWorld--A Wolfram Web Resource.

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