acosC＋1/2c=b,则2sinAcosC＋sinC=2sinB=2sin(A＋C)=2sinAcosC＋2cosAsinC,所以sinC=2cosAsinC,得cosA=1/2,A=60°.a/sinA=2R,周长=a＋2RsinB＋2RsinC=1＋2RsinB＋2Rsin(120°－B).展开即可