连接AF∵EF垂直平分AD∴FD=FA∴∠FDA=∠FAD∵∠FDA=∠B+∠BAD，∠EAD=∠FAC+∠CAD∴∠B+∠BAD=∠FAC+∠CAD∵∠BAD=∠CAD∴∠B=∠FAC在△ABF和△CAF中∵∠B=∠FAC，∠BFA=∠AFC∴△ABF∽△CAF∴FA/FC=FB/FA即FA^2=FC*FB∴FD^2=FC*FB
