∵AB is the diameter ⊙ O, and the chord CD⊥AB is at point E,

∴ The distance from the center O to the string CD is OE;

∠∠COB = 2∠CDB (the circumferential angle of the same arc is half of the central angle), ∠ CDB = 30,

∴∠cob=60；

In Rt△OCE,

OC=3cm，OE=OC？ cos∠COB，

∴OE=32.

So choose a.