Let A'B'C' be the circlecevian triangle of a point P. The circle with diameter AA’ and the circle {PBC} intersect at A". Define analogously B", C". The lines AA", BB", CC" concur at Q.
P being the circumcenter, Q is the point X(24).
P being the orthocenter, Q is the Prasolov point.
P being a Fermat point, Q is a Napoleon point.