Soddy Line


The triangle line that passes through the inner and outer Soddy centers S and S^'.

The Soddy line is central line L_(657) and has trilinear equation


It passes through Kimberling centers X_i for i=1 (incenter I), 7 (Gergonne point Ge), 20 (de Longchamps point L), 77, 170, 175 (outer Soddy center S^'), 176 (inner Soddy center S), 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 Ri), 1372 (outer Rigby point Ri^'), 1373 (inner Griffiths point Gr), 1374 (outer Griffiths point Gr^'), 1442, 1443, 1448, 1458, 1721, 1742, 1770, 2263, 2293, 2951, 3000, 3007, 3010, 3012, and 3019.

The points S^', I, S, 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).

See also

de Longchamps Point, Euler-Gergonne-Soddy Triangle, Euler Line, First Eppstein Point, Fletcher Point, Gergonne Point, Griffiths Points, Harmonic Range, Incenter, Rigby Points, Second Eppstein Point, Soddy Centers

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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.Vandeghen, A. "Soddy's Circles and the De Longchamps Point of a Triangle." Amer. Math. Monthly 71, 176-179, 1964.

Referenced on Wolfram|Alpha

Soddy Line

Cite this as:

Weisstein, Eric W. "Soddy Line." From MathWorld--A Wolfram Web Resource.

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