解:連接?$OC,$??$OA$?
∵?$AB、$??$AC$?是?$\odot O$?的切線
∴?$AO$?平分?$∠BAC,$??$OB⊥AB$?
∵?$AO$?平分?$∠BAC$?
∴?$∠BAO=∠CAO$?
∵?$OB⊥AB$?
∴?$∠ABD=∠ABO=90°$?
∵?$BD=BO,$??$∠ABD=∠ABO,$??$AB=AB$?
∴?$?ABD≌?ABO$?
∴?$∠DAB=∠OAB$?
∵?$∠DAB=∠OAB,$??$∠BAO=∠CAO,$??$∠DAC= 69°$?
∴?$∠DAB=23°$?
∵?$?ABD$?是直角三角形,?$∠DAB=23°$?
∴?$∠ADO=90°-23°=67°$?