證明：?$(1)$?連接?$OC，$?
?$∵C$?是?$\widehat{ACB}$?的中點(diǎn)，
?$∴\widehat{AC}=\widehat{BC}，$?
?$∴∠COD=∠COE.$?
?$∵OA=OB，$??$AD=BE，$?
?$∴OD=OE.$?
在?$△COD$?和?$△COE$?中，
?$\begin{cases}{CO=CO，}\\{∠COD=∠COE，}\\{OD=OE，}\end{cases}$?
?$∴△COD≌△COE(\mathrm {SAS})，$?
?$∴CD=CE.$?
?$(2)$?如圖，連接?$OM、$??$ON.$?
?$∵△COD≌△COE，$?
?$∴∠CDO=∠CEO，$??$∠OCD=∠OCE.$?
?$∵OC=OM=ON，$?
?$∴∠OCM=∠OMC，$??$∠OCN=∠ONC，$?
?$∴∠OMD=∠ONE.$?
?$∵∠ODC=∠DMO+∠MOD，$??$∠CEO=∠CNO+∠NOE，$?
?$∴∠MOD=∠NOE，$?
?$∴\widehat{AM}=\widehat{BN}.$?
