<Qua-2024-746>, hint

Let F be the midpoint of DE, then MF=1/2 AD. NC=1/2 CD.

Since <ABD=<DBC AD=DC  Hence MF=NC FN//MC, <FMC=<NCM=<FMC

MCNF is isosceles trapezoid and MCNF are concyclic, Since <FMC=<FBC=<DBC

BMFC is concyclic

Hence BMFNC is concyclic.