∵圆O是三角形ABC的内切圆,切点是D,E,F（D在BC上,F在AB上、E在AC上）
∴AF=AE,BD=BF,CD=CE,
∴2AE=AF+AE
=(AB-BF)+(AC-CE)
=AB+AC-(BF+CE)
=(AB+AC)-(BD+CD)
=AB+AC-BC
=(AB+AC+BC)-2BC
=18-12
=6