M and N are midpoints of two equal chords ab and cd.Prove angle bmn = angle dnm

join m and n to the centre of the circle.(point o)

so, omb=ond=90             [line joining centre of the circle and the centre of the chord is the perpendicular bisector of the chord]

omn=onm              [om=on, and in an isoceles triangle, angles opposite to equal sides are equal]

so,
omb=ond and omn=onm


omb-omn=ond-onm

therefore, bmn=dnm.