[APH]: In fact we can take any point P (instead of H) and any points O1,O2,O3 on the circumcircles of PBC,PCA,PAB, resp.
Then the circumcircles of the triangles
AO2O3, BO3O1, CO1O2
For a proof I offer the book:
R. G. SANGER: SYNTHETIC PROJECTIVE GEOMETRY (1939)