Let the inner and outer Soddy triangles of a reference triangle 
be denoted 
and 
, respectively. Similarly,
let the tangential triangles of 
and 
be denoted 
and 
, respectively. Then
the inner (respectively, outer) Rigby point Ri (respectively, 
)
is the perspector of 
and 
(respectively, 
and 
) (Oldknow 1996).
The Rigby points lie on the Soddy line. They have triangle center functions
 |  |  |
(1)
|
 |  |  |
(2)
|
which are Kimberling centers 
and 
, respectively.
Honsberger (1995) defines a different point which he calls the "Rigby point" 
. Let 
be an arbitrary chord of the circumcircle of a given triangle 
, and let 
be the Simson line pole
of the Simson line 
with respect to 
which is perpendicular
to 
. Then it also turns out that 
and 
. In addition, 
, 
, and 
with respect to 
.
As a result of these remarkable facts, it can be shown that the Simson lines 
, 
, and 
with respect to 
meet in the Rigby point 
. Moreover, the Simson lines 
, 
, and 
with respect to 
also meet in 
, and 
is the orthopole of 
, 
, and 
with respect to 
, and of 
, 
, and 
with respect to 
. Finally, 
is the midpoint of the orthocenters
of 
and 
(Honsberger 1996, p. 136).
