As shown in the figure, AB is the diameter of circle O, C is the point on circle O, passing point C is the tangent of circle O and intersects the extended line of AB at point E, OD perpendicular  AC at point D, if angle E = 30.0, CE = 6.0, then the value of OD is ()
Choices:
A:1
B:√{3}
C:2
D:2√{3}
Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.
Question: As shown in the figure, AB is the diameter of circle O, C is the point on circle O, passing point C is the tangent of circle O and intersects the extended line of AB at point E, OD perpendicular  AC at point D, if angle E = 30.0, CE = 6.0, then the value of OD is ()
Choices:
A:1
B:√{3}
C:2
D:2√{3}
Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.
Question: As shown in the figure, AB is the diameter of circle O, C is the point on circle O, passing point C is the tangent of circle O and intersects the extended line of AB at point E, OD perpendicular  AC at point D, if angle E = 30.0, CE = 6.0, then the value of OD is ()
Choices:
A:1
B:√{3}
C:2
D:2√{3}