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.