Basic Properties of circle I

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OA=OC, therefore OAC=OCA (isoceles triangle)
COB=2*CAB (exterior angle)
If arc BC = arc CD, then
BAC=CAD (angles subtended by equal arcs of a circle)
Since
CAD=OAC=OCA,
OC parallel to AD (alternate angles equal)

http://belinda.fileave.com/piccc.jpg
We have to assume that O is the centre of the circle, and we have to prove that
arc AD = arc DC (misprint in the question).
AB=BC (given)
OA=OC (radii)
OB=OB (common side)
triangle OAB and OCB are congruent.
AOD=BAO+ABO
COD=BCO+CBO
Therefore AOD=COD (exterior angles of congruent triangles)
arc AD = arc CD (arcs subtend equal angles at centre)