∫AC is the tangent of circle O, OA=OB,

∴OA⊥AC, ∠OAB=∠OBA=∠DAC, …(2 points)

AD is the midline of the hypotenuse of Rt△OAC,

∴AD=OD=DC=OA，

∴△AOD is an equilateral triangle, ∴△ AOD = 60,

Therefore ∠ ABC = 12 ∠ AOD = 30...(5 points)

(2) As can be seen from (1),

At Rt△AEB, ∠ EAB = ∠ ADB = 60,

∴ea= 12ab= 12×32bd=34bd，

EB=32AB=32×32BD=34BD, …(7 points)

According to secant theorem, EA2=EF×EB,

∴3 16BD2=EF×34BD，

∴ BD = 4ef...( 10)