As shown in the figure, the circle O is the circumscribed circle of triangle ABC, and the bisector of angle BAC and angle ABC intersects at point I. Extend AI and it intersects circle O at point D. Connect BD and DC. If the radius of circle O is 8.0, angle BAC = 120.0, then the length of DI is ()
Choices:
A:4√{3}+2
B:4√{3}+3
C:8√{3}+1
D:8√{3}
Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.
Question: As shown in the figure, the circle O is the circumscribed circle of triangle ABC, and the bisector of angle BAC and angle ABC intersects at point I. Extend AI and it intersects circle O at point D. Connect BD and DC. If the radius of circle O is 8.0, angle BAC = 120.0, then the length of DI is ()
Choices:
A:4√{3}+2
B:4√{3}+3
C:8√{3}+1
D:8√{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, the circle O is the circumscribed circle of triangle ABC, and the bisector of angle BAC and angle ABC intersects at point I. Extend AI and it intersects circle O at point D. Connect BD and DC. If the radius of circle O is 8.0, angle BAC = 120.0, then the length of DI is ()
Choices:
A:4√{3}+2
B:4√{3}+3
C:8√{3}+1
D:8√{3}