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, then the length of DI is ()
  Choices:
  A:4√{3}+2
  B:4√{3}+3
  C:8√{3}+1
  D:8√{3}
query_wo: 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, then the length of DI is ()
  Choices:
  A:4√{3}+2
  B:4√{3}+3
  C:8√{3}+1
  D:8√{3}
query_cot: 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, then the length of DI is ()
  Choices:
  A:4√{3}+2
  B:4√{3}+3
  C:8√{3}+1
  D:8√{3}
question_for_eval: 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, then the length of DI is ()
  Choices:
  A:4√{3}+2
  B:4√{3}+3
  C:8√{3}+1
  D:8√{3}