如图,在三角形ABC中,F是AC上的点,且AF:FC=1:2,G为BF的中点,AG的延长线交B于E,求BE:EC

问题描述:

如图,在三角形ABC中,F是AC上的点,且AF:FC=1:2,G为BF的中点,AG的延长线交B于E,求BE:EC

过点F作FH‖AE,交BC于点H.
则有:BE∶EH = BG∶GF = 1 ,EH∶HC = AF∶FC = 1∶2 ,
所以,BE = EH = (1/2)HC ,BH = BE+EH = HC = (1/2)BC ;
可得:BE = (1/4)BC ,EC = BC-BE = (3/4)BC ,
所以,BE∶EC = 1∶3 .