△EMO∽△ONF EM/ON=MO/NF EM*FN=OM*ON△AEM∽△FBN EM/BN=AM/FN EM*FN=BN*AM∴OM*ON=BN*AM 设AO=BO=1 AM=X ON=Y 则MO=1-X NB=1-Y∴（1-x)*y=(1-y)*x ∴X=Y 即是AM=OB
