de Longchamps Ellipse


The de Longchamps ellipse of a triangle DeltaABC is the conic circumscribed on the incentral triangle and the Cevian triangle of the isogonal mittenpunkt X_(57). (Since a conic is uniquely determined by five points, the conic is already specified with only five of these six points.)

The de Longchamps ellipse is centered at the incenter I of the reference triangle, and has trilinear equation


which can also be written


It passes through the points X_(244), X_(2170), and X_(2611) (Weisstein, Oct. 17 and Nov. 22, 2004).

See also

Cevian Triangle, de Longchamps Circle, Incentral Triangle, Isogonal Mittenpunkt

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Catalan, E. "Note sur l'ellipse de Longchamps." J. Math. Spéciales 4, 28-30, 1893.

Referenced on Wolfram|Alpha

de Longchamps Ellipse

Cite this as:

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

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