在三角形abc中,D是AB的中点,过点D的直线交AC于E,交BC的延长线于F.(1)求证BF/CF=AE/EC

可以的.证明：作DG平行AC交BC于G,则DG=1/2 AC,GC=1/2 BC.由△CEF相似于△GDF,则：CE/DG=CF/GF则：CE/(1/2AC)=CF/(HC+CF)CE/(1/2AE+1/2CE)=CF/(1/2BC+1/2CF+1/2CF)将1/2销去,得：CE/(AE+CE)=CF/(BC+CF+CF)CE/(AE+CE)=...