證明: (1)在$\triangle ABO$和$\triangle DCO$中，
$\begin{cases}\angle AOB=\angle DOC \\\angle ABO=\angle DCO \\AB = DC\end{cases}$
$\therefore \triangle ABO\cong\triangle DCO(AAS)。$
(2)$\because \triangle ABO\cong\triangle DCO，$$\therefore \angle A=\angle D，$$OA = OD，$$OB = OC，$$\therefore OB + OD=OA + OC，$即$BD = AC。$
在$\triangle ABC$和$\triangle DCB$中，
$\begin{cases}AB = DC \\BC = CB \\AC = DB\end{cases}$
$\therefore \triangle ABC\cong\triangle DCB(SSS)，$$\therefore \angle ABC=\angle DCB，$$\therefore \angle ABC-\angle ABO=\angle DCB-\angle DCO，$$\therefore \angle OBC=\angle OCB。$
