chords ge and md of circle o are both extended to inserted at n. if on bisects <gnm

Question

please put the statements and reason

Answer 1

<MNO=<ONG (given)

GO=MO=EO=DO (radii)

<GON=<MON (symmetry of the bisector)

<OEG=<OGE (isosceles triangle OEG formed by radii GO and EO)

Similarly <OMD=<ODM.

∆s NOD and NOE are congruent as are GOE and MOD, so the chords MD and GE have equal length.

The question doesn’t ask us to find or prove anything.