<Tri-2026-2320>, hint

Let S be the point of concurrence  of  chords AD,BE,CF and O the center of circle.

Since OP, OQ OR are perpendicular to AD,BE,CF respectively O, P, Q,R are concyclic

Let <CSD=x, <CSF=y, <ASF=z, then by angle chasing <PRQ=x, <PQR=z, <QPR=y

<GHD=x, <GDH=y, <DGH=z