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# Gergonne Line

The Gergonne line is Oldknow's (1996) term for the perspectrix of a contact triangle and its reference triangle . It is determined by the Nobbs points , , and .

In addition to the Nobbs points, the Fletcher point (intersection with the Soddy line) and Evans point (intersection with the Euler line) also lie on the Gergonne line. Furthermore, the Soddy line and Gergonne line are perpendicular (Oldknow 1996).

The Gergonne line is central line and has trilinear equation

where is the semiperimeter of . It passes through Kimberling centers for , 514, 650, 665, 1323 (Fletcher point), and 1375 (Evans point), 1465, 1638, 3002, 3004, 3008, and 3015.

The Gergonne line is the perspectrix of the contact triangle and reference triangle, as well as the excentral triangle and medial triangle.

The angle between the orthic axis and Gergonne line is equal to that between the Euler line and the Soddy line (F. Jackson, pers. comm., Nov. 2, 2005).

Contact Triangle, Euler-Gergonne-Soddy Triangle, Euler Line, Evans Point, Fletcher Point, Nobbs Points, Soddy Line, Tangential Triangle

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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.

Gergonne Line

## Cite this as:

Weisstein, Eric W. "Gergonne Line." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/GergonneLine.html