Let A', B', C' be the cevian traces of P. Let Ga, Gb, Gc be the centroids of AB'C', BC'A', CA'B'. The lines AGa, BGb, CGc concur at a point Q.
When P is the orthocenter, Q is the symmedian point.
When P is the Gergonne point, Q is the incenter.
When P is the Nagel point, Q is the Mittenpunkt.
Another particular case is r611.