The Soddy line is the triangle line that passes through the inner and outer Soddy centers 
and 
.
The Soddy line is central line 
and has trilinear equation
 |
It passes through Kimberling centers 
for 
(incenter 
), 7 (Gergonne
point Ge), 20 (de Longchamps point 
), 77, 170, 175 (outer
Soddy center 
), 176 (inner
Soddy center 
), 269, 279, 347, 390, 481 (first Eppstein point), 482 (second
Eppstein point), 962 (the Longuet-Higgins point), 990, 991, 1042, 1044, 1323
(Fletcher point Fl), 1371 (inner Rigby
point 
), 1372 (outer Rigby point 
), 1373 (inner Griffiths
point 
), 1374 (outer Griffiths
point 
), 1442, 1443, 1448, 1458, 1721, 1742, 1770, 2263,
2293, 2951, 3000, 3007, 3010, 3012, and 3019.
The points 
, 
, 
,
and Ge form a harmonic range on the Soddy
line (Vandeghen 1964, Oldknow 1996). There are a total of 22 harmonic
ranges for sets of four points out of these 10 (Oldknow 1996). The Soddy line
intersects the Euler line
in the de Longchamps point and the Gergonne
line in the Fletcher point. Furthermore, the
Soddy line and Gergonne line are perpendicular
(Oldknow 1996).
The Soddy line is the radical line of the GEOS circle and Euler-Gergonne-Soddy circle.
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).
Let 
be the foot of the altitude
from 
, let 
, and let 
be the semiperimeter. If
the Soddy line meets this altitude in a unique finite
point 
, then
 |
The analogous formulas hold at 
and 
(F. M. Jackson, pers. comm., Sep. 13, 2006 and June 3, 2008).
