Question

C,D是线段AB上的两点.AC=5/9BC,AD=9/5DB.已知CD=2,求线段AB的长

Answer 1

已知,AC = (5/9)BC ,AD = (9/5)DB ,

可得：AC/CB = 5/9 = DB/AD ,

则有：AC/(AC+CB) = DB/(DB+AD) = 5/(5+9) ,

即有：AC/AB = DB/AB = 5/14 ,

所以,AC = DB = (5/14)AB ,

可得：CD = AB-AC-DB = (2/7)AB ,

所以,AB = (7/2)CD = 7 .