如图,AD是△ABC的角平分线,若AB=2AC.则S△ABD:S△ACD=_.

问题描述:

如图,AD是△ABC的角平分线,若AB=2AC.则S△ABD:S△ACD=______.


过D作DM⊥AC于M,DN⊥AB于N,
∵AD是△ABC的角平分线,
∴DM=DN,
∴S△ABD:S△ACD=(

1
2
AB×DN):(
1
2
AC×DM)=AB:AC=2AC:AC=2,
故答案为:2.