Second Droz-Farny Circle


Consider the circles centered on the midpoints of the sides of a reference triangle and passing though the orthocenter H. These circles cut the sides in six points lying on a circle D_2 known as the second Droz-Farny circle.

It has radius


equal to that of the first Droz-Farny circle D_1, but center is the circumcenter O instead of the orthocenter H. The second Droz-Farny circle has circle function


corresponding to the symmedian point K.

No Kimberling centers lie on the second Droz-Farny circle.

See also

Central Circle, Droz-Farny Circles, First Droz-Farny Circle

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Droz-Farny, A. "Notes sur un théorème de Steiner." Mathesis 21, 22-24, 1901.Goormaghtigh, R. "Droz-Farny's Theorem." Scripta Math. 16, 268-271, 1950.Honsberger, R. "The Droz-Farny Circles." §7.4 (ix) in Episodes in Nineteenth and Twentieth Century Euclidean Geometry. Washington, DC: Math. Assoc. Amer., pp. 69-72, 1995.Johnson, R. A. Modern Geometry: An Elementary Treatise on the Geometry of the Triangle and the Circle. Boston, MA: Houghton Mifflin, pp. 256-258, 1929.

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Second Droz-Farny Circle

Cite this as:

Weisstein, Eric W. "Second Droz-Farny Circle." From MathWorld--A Wolfram Web Resource.

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