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) | |||
| (2) |
where is the circumcenter,
is the orthocenter,
,
,
, and
is Conway triangle notation,
is the area of the reference triangle, and
| (3) |
Its circle function interestingly corresponds to the same triangle center as its center: .
Its -power is given by
| (4) |
(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).