Given two cyclologic triangles 
and 
, the point 
at which the circles through 
, 
, and 
are concurrent is the
cyclologic center of 
with respect to 
.
The reciprocal point 
,
meaning the counterpart obtained by interchanging the two triangles, is defined by
the circles through 
, 
, and 
. It is the cyclologic center of 
with respect to 
. The term "cyclologic center" is recorded
by Lozada (2025) and is defined in this form by Rabinowitz and Suppa (2026, p. 105).
Cyclologic Center
See also
Cyclologic TrianglesExplore with Wolfram|Alpha
References
Lozada, C. E. "Alphabetical Index of Terms in ETC." 2025. https://faculty.evansville.edu/ck6/encyclopedia/Alphabetical_Index.html.Rabinowitz, S. and Suppa, E. "Cyclologic Triangles Formed by Three Isodynamic Points." To appear in Int. J. Comput. Discovered Math., 2026. https://www.researchgate.net/publication/411174028_Cyclologic_Triangles_Formed_by_Three_Isodynamic_Points.Cite this as:
Weisstein, Eric W. "Cyclologic Center." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/CyclologicCenter.html