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 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).

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. Monthly103, 319-329, 1996.