∵OA＝AC,∴∠AOC＝∠OCA,而∠OCA＝45°,∴∠AOC＝45°,∴OA⊥AC.
∵OA＝AB,∴∠AOB＝∠OBA,而∠OBA＝45°,∴∠AOB＝45°,∴OA⊥AB.
由OA⊥AC、OA⊥AB、AC∩AB＝A,∴AO⊥平面ABC.