Consider the circles centered on the midpoints of the sides of a reference triangle and passing though the orthocenter
It has radius
equal to that of the first Droz-Farny circle circumcenter orthocenter circle function
(3)
corresponding to the symmedian point
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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References 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. Johnson, R. A. Modern
Geometry: An Elementary Treatise on the Geometry of the Triangle and the Circle. Referenced on Wolfram|Alpha Second Droz-Farny Circle
Cite this as:
Weisstein, Eric W. "Second Droz-Farny Circle."
From MathWorld https://mathworld.wolfram.com/SecondDroz-FarnyCircle.html
Subject classifications
.
These circles cut the sides in six points lying on a circle 
known as the second Droz-Farny circle.
,
but center is the circumcenter 
instead of the orthocenter 
.
The second Droz-Farny circle has circle function
.
