如图：连接AF，∵EF垂直平分AD，∴FA=FD．∠FAD=∠FDA，∵AD平分∠BAC，∴∠BAD=∠CAD．在△FAC和△FBA中，∠AFC=∠BFA，∠ACF=∠B+2∠BAD=∠FDA+∠BAD=∠FAD+∠BAD=∠BAF．∴△ACF∽△BAF，∴CFAF=AFBF．∴AF2=BF•...