prove if one angle subtended by two chords of a circle equal the chords are equal

in this circle the angle AOB and angle DOC are equal as it is given

to prove that the chords are equal we have to show that the triangles,AOB and DOC are congruent.

therefore,in triangle AOB and DOC,

AO=DO (radius)

angle AOB=angle DOC (given)

BO=CO  (radius)

therefore,Triangle AOB and triangle DOC are congruent by SAS congruence criterion 

thus,AB=DC by CPCT(Congruent Parts of Congruent Triangles)