Let X, P be two points; XaXbXc, PaPbPc
their circumcevian triangles; AxBxCx the circumcevian triangle of P with
respect to XaXbXc. The triangles PaPbPc, AxBxCx are perspective with center
Q.

P being the incenter and X being
the circumcenter, Q is the point X(56)

P being the circumcenter and X being
the incenter, Q is the Bevan point

P being the circumcenter and X being
the centroid, Q is the point X(376)

P being the circumcenter and X being
the orthocenter, Q is the De Longchamps point

P being the orthocenter and X being
the circumcenter, Q is the point X(24)