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).