Triangle OFD is similar to triangle AFE,
AF/DF=EF/F0=AE/DO
Triangle ODG is similar to triangle AEG,
AE/DO=AG/OG
Connect BC, triangle ABC is similar to triangle age.
AC/AB=AE/AG
Triangle ODG is similar to triangle AEG.
AE/AG=OD/OG=2/5
OB=OA=OD
So AG/OG=(AO+OG)/OG=7/5.
So AF/DF=AE/DO=AG/OG=7/5.