∵AD是△ABC的外角∠EAC的平分线，∠EAC=120°，∴∠CAD=∠EAD=∠EAB=60°，∴∠BAC=60°．∵∠BFA=90°，∴AB是此圆的直径，∴∠ACB=90°．∴AB＝ BC sin60° = 6 3 2 =4 3 ．∵∠D=∠FAB-∠ABC=30°．∴AD=AB=4 3 ．故答案为4 3 ．
