解答：证法一：在△ABC和△DCB中，∵AB=CD，∠ABC=∠BCD，BC边公用，∴△ABC≌△DCB．∴AC=DB，且∠ACB=∠DBC．∴OB=OC．∴OA=OD；证法二：（同证法一）∴△ABC≌△DCB．∴∠ACB=∠DBC．∴∠ABO=∠DCO．又∵∠AOB=∠DOC，∴△AOB≌△DOC．∴OA=OD．
