直线l分别交三角形ABC的边BC,CA,AB于点D,E,F,且AF=1/3AB,BD=5/2BC,求EC/AE

问题描述:

直线l分别交三角形ABC的边BC,CA,AB于点D,E,F,且AF=1/3AB,BD=5/2BC,求EC/AE

BD=5/2BC,是不是BD=2.5BC
若是,则EC/AE=6/5

过点A作AG∥BC交直线l于点G∵AF=1/3AB∴AF:AB=1:3 AF:BF=1:2∵BD=5/2BC ∴BC:BD=2:5 BC:CD=2:3设BC=2m 则 CD=3m BD=5m∵AG∥BC∴AG:BD=AF:BF=1:2∴AG:5m=1:2AG=2.5m∵AG∥BC∴EC:AE=CD:AG=3m:2.5m=6...