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Euler-Gergonne-Soddy Triangle


Euler-Gergonne-SoddyTriangle

The Euler-Gergonne-Soddy triangle is the right triangle DeltaZFlEv created by the pairwise intersections of the Euler line L_E, Soddy line L_S, and Gergonne line L_G. (The triangle is always right since the Soddy and Gergonne lines always intersect perpendicularly.) The vertices of this triangle are the de Longchamps point Z (L_S intersection L_E), Fletcher point Fl (L_G intersection L_S), and Evans point Ev (L_G intersection L_E) (Oldknow 1996).

It is not in perspective with DeltaABC.

The circumcircle of the Euler-Gergonne-Soddy triangle is the Euler-Gergonne-Soddy circle.


See also

de Longchamps Point, Euler Line, Evans Point, Fletcher Point, Gergonne Line, Soddy Line

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References

Beauregard, R. A. and Suryanarayan, E. R. "Another Look at the Euler-Gergonne-Soddy Triangle." Math. Math. 76, 385-390, 2003.Oldknow, A. "The Euler-Gergonne-Soddy Triangle of a Triangle." Amer. Math. Monthly 103, 319-329, 1996.

Referenced on Wolfram|Alpha

Euler-Gergonne-Soddy Triangle

Cite this as:

Weisstein, Eric W. "Euler-Gergonne-Soddy Triangle." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Euler-Gergonne-SoddyTriangle.html

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