延长AI交BC于D,∵I是△ABC的内心,∴BD/DC=AB/AC=c/b,∴BD=ac/(b+c),bBD=cDC,在△ABD中,AI是∠ABD的平分线,∴AI/ID=BA/BD=(b+c)/a,∴aAI=(b+c)ID,∴aAI+bBI+cCI =(b+c)ID+bBI+cCI =b(BI+ID)+c(CI+ID) =bBD+cCD =cDC+c...