因为圆O是三角形ABC的内切圆,切点是D,E,F
所以AF=AE,BD=BF,CD=CE,
所以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