The Soddy line of a triangle is the line that goes through the centers of the two Soddy circles of that triangle. The Soody line intersects the

Euler line In geometry, the Euler line, named after Leonhard Euler (), is a line determined from any triangle that is not equilateral. It is a central line of the triangle, and it passes through several important points determined from the triangle, inclu ...

de Longchamps point In geometry, the de Longchamps point of a triangle is a triangle center named after French mathematician Gaston Albert Gohierre de Longchamps. It is the reflection of the orthocenter of the triangle about the circumcenter.. Definition Let the ...

und the Gergonne line in the ''Fletcher point''. It is also perpendicular to the Gergonne line and together all three lines form the Euler-Gergonne-Soddy triangle. The

Gergonne point In geometry, the incircle or inscribed circle of a triangle is the largest circle that can be contained in the triangle; it touches (is tangent to) the three sides. The center of the incircle is a triangle center called the triangle's incenter. ...

and the

incenter In geometry, the incenter of a triangle is a triangle center, a point defined for any triangle in a way that is independent of the triangle's placement or scale. The incenter may be equivalently defined as the point where the internal angle bisec ...

of the triangle are located on the on the Soddy line as well. The line is named after Nobel laureate

Frederick Soddy Frederick Soddy FRS (2 September 1877 – 22 September 1956) was an English radiochemist who explained, with Ernest Rutherford, that radioactivity is due to the transmutation of elements, now known to involve nuclear reactions. He also prove ...

, who published a proof of a special case of

Descartes' theorem In geometry, Descartes' theorem states that for every four kissing, or mutually tangent, circles, the radii of the circles satisfy a certain quadratic equation. By solving this equation, one can construct a fourth circle tangent to three given, mu ...

about tangent circles as a poem in

Nature Nature, in the broadest sense, is the physics, physical world or universe. "Nature" can refer to the phenomenon, phenomena of the physical world, and also to life in general. The study of nature is a large, if not the only, part of science. ...

in 1936.

References

* Zuming Feng: ''Why Are the Gergonne and Soddy Lines Perpendicular? A Synthetic Approach''. In: ''Mathematics Magazin'', Band 81, Nr. 3, Juni 2008, S. 211-214
JSTOR
*Roger Alperin: ''The Gergonne and Soddy lines''. In: ''Elemente der Mathematik'',. Band 70, Nr. 1, 2015, S. 1-6
online

External links

* {{MathWorld, title=Soddy line, urlname=SoddyLine Triangle geometry