梯形ABCD中DC平行AB,点E是BC延长线上一点,AE和BD相交于点F,AB:CD=a,BC:BE=b,(a>0,b>0),则AF:EF的值是

Question

梯形ABCD中DC平行AB,点E是BC延长线上一点,AE和BD相交于点F,AB:CD=a,BC:BE=b,(a>0,b>0),则AF:EF的值是

Answer 1

过E作EG∥DC交BD延长线于G
BC/BE=b
DC/GE=b
DC=b*GE
△ABF∽△EFG
AF/FE=AB/GE
AB/CD=a
AB=a*CD=a*b*GE
AF/EF=(a*b*GE)/GE=a*b
AF=abEF
AE=AF+EF=(ab+1)EF
AE/EF=(ab+1)EF/EF=ab+1