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).