The reflection circle, a term coined here for the first time, is the circumcircle of the reflection triangle. It has center at Kimberling center , which is the -Ceva conjugate of .
The radius is given by
(1)
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(2)
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where is the circumcenter, is the orthocenter, , , , and is Conway triangle notation, is the area of the reference triangle, and
(3)
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Its circle function interestingly corresponds to the same triangle center as its center: .
Its -power is given by
(4)
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(P. Moses, pers. comm., Feb. 3, 2005).
No Kimberling centers lie on it. However, the anticomplements of and lie on it, as do the reflection of in and in (P. Moses, pers. comm., Jan. 31, 2005).