∵∠ABC＝90∴AC＝√（AB²+BC²）＝√（144+256）＝20S△ABC＝BC×AB/2＝16×12/2＝96∵AO平分∠BAC,OD⊥AC,OE⊥AB∴OD＝OE∵CO平分∠ACB,OD⊥AC,OF⊥BC∴OD＝OF∴OD＝OE＝OF∴S△AOB＝AB×OE/2＝AB×OD/2S...