如下图,在三角形ABC中,EF两点在边AB上,AE=BF,HE//CA//GF,H,G两点在BC边上,EH,FG,

问题描述:

如下图,在三角形ABC中,EF两点在边AB上,AE=BF,HE//CA//GF,H,G两点在BC边上,EH,FG,
AC之间有什么关系?说明理由

HE//GFBE/BF=HE/GF.1又AE=BF所以:BE=AB-AE=AB-BF.22代入1有:(BA-BF)/BF=HE/GFBA/BF -1=HE/GF.3HE//CABE/BA=HE/AC同上有:(BA-BF)/BA=HE/AC1-BF/BA=HE/AC.4于是利用3,4式消去BF,BA有:(HE/GF +1)(1-HE/AC)=1上...