如图,已知△ABC,点D,E分别在BC,AC上,BD=2CD,AE=CE,AD,BE相交于F点,S△ABF=10,求S△AEFhttp://wenwen.soso.com/z/q273463521.htm

Question

如图,已知△ABC,点D,E分别在BC,AC上,BD=2CD,AE=CE,AD,BE相交于F点,S△ABF=10,求S△AEF
http://wenwen.soso.com/z/q273463521.htm

Answer 1

连接FC
得到△AFE
∵AE=EC
∴S△AFE=S△FEC
∵AE=EC
∴S△AEB=S△EBC
∵S△AFE=S△FEC
∴S△AFB=S△BFC=10
∵BD=2DC
∴S△DCF=1/3*S△BFC=10/3
设S△AFE为X
则(2X+10/3)*2=20-10/3
4X+20/3=50/3
4X=10
X=2.5