question: In the diagram above, There are two triangles ABC an BDE, where BE is on AB. Angle A is congruent to angle BED, and angle C is congruent to angle D. If the ratio of the length of AB to the length of EB is 5:1, and the area of the triangle BED is 5*a^2 + 10, what is the area of triangle ABC?
  Choices:
  A.5*a^2 + 10
  B.25*a^2 + 50
  C.25*a^2 + 100
  D.125*a^2 + 250
  E.cannot be determined
query_wo: Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.
  Question: In the diagram above, There are two triangles ABC an BDE, where BE is on AB. Angle A is congruent to angle BED, and angle C is congruent to angle D. If the ratio of the length of AB to the length of EB is 5:1, and the area of the triangle BED is 5*a^2 + 10, what is the area of triangle ABC?
  Choices:
  A.5*a^2 + 10
  B.25*a^2 + 50
  C.25*a^2 + 100
  D.125*a^2 + 250
  E.cannot be determined
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 diagram above, There are two triangles ABC an BDE, where BE is on AB. Angle A is congruent to angle BED, and angle C is congruent to angle D. If the ratio of the length of AB to the length of EB is 5:1, and the area of the triangle BED is 5*a^2 + 10, what is the area of triangle ABC?
  Choices:
  A.5*a^2 + 10
  B.25*a^2 + 50
  C.25*a^2 + 100
  D.125*a^2 + 250
  E.cannot be determined
question_for_eval: In the diagram above, There are two triangles ABC an BDE, where BE is on AB. Angle A is congruent to angle BED, and angle C is congruent to angle D. If the ratio of the length of AB to the length of EB is 5:1, and the area of the triangle BED is 5*a^2 + 10, what is the area of triangle ABC?
  Choices:
  A.5*a^2 + 10
  B.25*a^2 + 50
  C.25*a^2 + 100
  D.125*a^2 + 250
  E.cannot be determined