<Tri-2023-2075>, hint

Let H be the orthocenter and D' the intersection of CH and AB.

Since A,B,E,F are concyclic and D is the center of circle O'(ABEF)  DB=DE=DF=DA ( radius of O')<DEF=<DFE=<ACB . Let M be the midpoint of EF and H' on AE such that D'H//DH'

AEH'D are concyclic (<D'HE=<DH'E). CD cut  EF at J'. Triangles ACE and DFM are similar

DJ' cut the circumcircle of BDE at P and AP cut BC at J. Since the center of the triangle DEF lies on DM <MDC=<ODC Let"s prove <PAE=<JAE=<MDC and triangles DFJ' and ACJ are sinmilar.