已知,三角形ABC中,D在BC上,BD:DC=2:3,E在AD上,且AE:ED=3:4,BE交AC于点F,求AF:CF的值.

问题描述:

已知,三角形ABC中,D在BC上,BD:DC=2:3,E在AD上,且AE:ED=3:4,BE交AC于点F,求AF:CF的值.

证明:过D作DG//BF交AC于G.在△CDG和△CBF中,有△CDG∽△CBF CG:CF=CD:CB=3:5,CG:FG=CG:(CF-CG)=3:2 在△AEF和△ADG中,有△AEF∽△ADG AE:AD=AF:AG=3:7,AF:FG=AF:(AG-AF)=3:4 AF:CF=(AF:FG)*(FG:CF)=(3:4)*(2:5)=3:10