question: In the figure above, the circle has center P and radius r. Lines AB and AC are tangent to the circle. If M is the midpoint of segment AC and the measure of angle PMC equals the measure of angle MPC, what is the length, in terms of r, of segment PA?
  Choices:
  A.r + 1
  B.2*r
  C.r*\sqrt{2}
  D.r*\sqrt{3}
  E.r*\sqrt{5}
query_wo: Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.
  Question: In the figure above, the circle has center P and radius r. Lines AB and AC are tangent to the circle. If M is the midpoint of segment AC and the measure of angle PMC equals the measure of angle MPC, what is the length, in terms of r, of segment PA?
  Choices:
  A.r + 1
  B.2*r
  C.r*\sqrt{2}
  D.r*\sqrt{3}
  E.r*\sqrt{5}
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: In the figure above, the circle has center P and radius r. Lines AB and AC are tangent to the circle. If M is the midpoint of segment AC and the measure of angle PMC equals the measure of angle MPC, what is the length, in terms of r, of segment PA?
  Choices:
  A.r + 1
  B.2*r
  C.r*\sqrt{2}
  D.r*\sqrt{3}
  E.r*\sqrt{5}
question_for_eval: In the figure above, the circle has center P and radius r. Lines AB and AC are tangent to the circle. If M is the midpoint of segment AC and the measure of angle PMC equals the measure of angle MPC, what is the length, in terms of r, of segment PA?
  Choices:
  A.r + 1
  B.2*r
  C.r*\sqrt{2}
  D.r*\sqrt{3}
  E.r*\sqrt{5}