id
int64 0
399
| depth
stringclasses 4
values | problem_version
stringclasses 1
value | answer_type
stringclasses 2
values | conversations
listlengths 2
2
| prompt_pre
stringclasses 4
values | image
dict | prompt_post
stringclasses 2
values | language
stringclasses 2
values |
|---|---|---|---|---|---|---|---|---|
0
|
depth0
|
text_lite
|
multi_choice
|
[
{
"from": "human",
"value": "First perform reasoning, then select the answer from the choices in the following format: Answer: xxx.\n<image>\nAB equals to 2. Please provide the length of DC in shape ABCD.\nChoices:\nA.2\nB.12/5\nC.10*√(3)/3\nD.2*√(2)/3"
},
{
"from": "gpt",
"value": "Considering that AB measures 2. Because ABCD is a rectangle, the opposite sides are equal. Hence, DC is also 2. Answer: A"
}
] |
First perform reasoning, then select the answer from the choices in the following format: Answer: xxx.
<image>
|
{
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"path": "depth0_en/0/1_text.jpg"
}
|
Answer:
|
English
|
1
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depth0
|
text_lite
|
multi_choice
|
[
{
"from": "human",
"value": "First perform reasoning, then select the answer from the choices in the following format: Answer: xxx.\n<image>\nSide CD developing into a semi-circle beyond the rectangle. AD is equal to √(2). How much is the perimeter of ABCD?\nChoices:\nA.√(6)*(2 + π + 4*√(2))/6\nB.1 + π/2 + 2*√(2)\nC.1\nD.4/3 + 2*π/3 + 8*√(2)/3"
},
{
"from": "gpt",
"value": "CD is the opposite side of AB, so CD is also 1. The semicircle from C to D has CD as its diameter, with a length of 1 * π/2 = π/2. The total perimeter of the shape is AB + AD + BC + the semicircle CD, which equals 1 + √(2) + √(2) + π/2 = 1 + π/2 + 2*√(2). Answer: B"
}
] |
First perform reasoning, then select the answer from the choices in the following format: Answer: xxx.
<image>
|
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"path": "depth0_en/1/2_text.jpg"
}
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Answer:
|
English
|
2
|
depth0
|
text_lite
|
multi_choice
|
[
{
"from": "human",
"value": "First perform reasoning, then select the answer from the choices in the following format: Answer: xxx.\n<image>\nABCD conforms a parallelogram. Angle ABC is 60°, CB measures 5. What is the total area of the shape ABCD?\nChoices:\nA.25*√(3)/2\nB.10*√(3)\nC.125*√(3)/8\nD.125*√(3)/6"
},
{
"from": "gpt",
"value": "Because parallelogram ABCD has an angle ABC of 60°, the area can be found using AB * CB * sin(60°), resulting in 5 * 5 * √(3)/2 = 25*√(3)/2. Answer: A"
}
] |
First perform reasoning, then select the answer from the choices in the following format: Answer: xxx.
<image>
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"path": "depth0_en/10/11_text.jpg"
}
|
Answer:
|
English
|
3
|
depth0
|
text_lite
|
multi_choice
|
[
{
"from": "human",
"value": "First perform reasoning, then select the answer from the choices in the following format: Answer: xxx.\n<image>\nSquare ABCD includes an inscribed circle. AB totals 81. What is the area of the entire inscribed circle?\nChoices:\nA.6561*π/5\nB.2187*√(3)*π/2\nC.6561*π/4\nD.6561*√(2)*π/4"
},
{
"from": "gpt",
"value": "The radius of the circle inscribed in square ABCD is AB/2 = 81/2, giving an area of (81/2)^2 * π = 6561*π/4. Answer: C"
}
] |
First perform reasoning, then select the answer from the choices in the following format: Answer: xxx.
<image>
|
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"path": "depth0_en/11/12_text.jpg"
}
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Answer:
|
English
|
4
|
depth0
|
text_lite
|
multi_choice
|
[
{
"from": "human",
"value": "First perform reasoning, then select the answer from the choices in the following format: Answer: xxx.\n<image>\nSide CD converts into a semi-circle. AD amounts to 2. What is the full area of the shape ABCD?\nChoices:\nA.π + 6\nB.π/2\nC.√(2)*(π + 8)/10\nD.π/2 + 4"
},
{
"from": "gpt",
"value": "For rectangle ABCD, the area is AB * AD = 2 * 2, resulting in 4. The area of the semicircle with CD as the diameter is (AB/2)^2 * π/2 = π/2. The total combined area is 4 + π/2 = π/2 + 4. Answer: D"
}
] |
First perform reasoning, then select the answer from the choices in the following format: Answer: xxx.
<image>
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"path": "depth0_en/12/13_text.jpg"
}
|
Answer:
|
English
|
5
|
depth0
|
text_lite
|
multi_choice
|
[
{
"from": "human",
"value": "First perform reasoning, then select the answer from the choices in the following format: Answer: xxx.\n<image>\nABC is an isosceles triangle where the lengths of AB and BC are equal. Angle CBA is 120°. In the isosceles triangle ABC, what are the measures of angle BAC and angle ACB?\nChoices:\nA.30\nB.10\nC.15\nD.22.5"
},
{
"from": "gpt",
"value": "With ABC being an isosceles triangle with vertex angle B of 120°, angles BAC and ACB are each (180° - 120°) / 2 = 30°. Answer: A"
}
] |
First perform reasoning, then select the answer from the choices in the following format: Answer: xxx.
<image>
|
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"path": "depth0_en/13/14_text.jpg"
}
|
Answer:
|
English
|
6
|
depth0
|
text_lite
|
multi_choice
|
[
{
"from": "human",
"value": "First perform reasoning, then select the answer from the choices in the following format: Answer: xxx.\n<image>\nAB is equal to 65. How long is DC in shape ABCD?\nChoices:\nA.195/4\nB.65*√(2)/6\nC.65*√(2)\nD.65"
},
{
"from": "gpt",
"value": "Since AB is 65 and ABCD is a rectangle, the opposite sides are equal. Therefore, DC is also 65. Answer: D"
}
] |
First perform reasoning, then select the answer from the choices in the following format: Answer: xxx.
<image>
|
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"path": "depth0_en/14/15_text.jpg"
}
|
Answer:
|
English
|
7
|
depth0
|
text_lite
|
multi_choice
|
[
{
"from": "human",
"value": "First perform reasoning, then select the answer from the choices in the following format: Answer: xxx.\n<image>\nABC takes on a sector shape. AB measures 100. Can you tell me the length of arc AC in sector ABC?\nChoices:\nA.15*π\nB.25*π\nC.75*√(2)*π\nD.50*π/3"
},
{
"from": "gpt",
"value": "The sector's central angle measures 45° which equals π/4, and the radius AB is 100. Therefore, the arc length AC equals 100 * π/4 = 25*π. Answer: B"
}
] |
First perform reasoning, then select the answer from the choices in the following format: Answer: xxx.
<image>
|
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}
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Answer:
|
English
|
8
|
depth0
|
text_lite
|
multi_choice
|
[
{
"from": "human",
"value": "First perform reasoning, then select the answer from the choices in the following format: Answer: xxx.\n<image>\nAD amounts to 11. What is the side length DC in the shape ABCD?\nChoices:\nA.8*√(3)/5\nB.16/3\nC.4*√(3)/3\nD.8"
},
{
"from": "gpt",
"value": "Given that AB has a length of 8. As ABCD is a rectangle, the opposite sides are equal. Therefore, DC is also 8. Answer: D"
}
] |
First perform reasoning, then select the answer from the choices in the following format: Answer: xxx.
<image>
|
{
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"path": "depth0_en/16/17_text.jpg"
}
|
Answer:
|
English
|
9
|
depth0
|
text_lite
|
multi_choice
|
[
{
"from": "human",
"value": "First perform reasoning, then select the answer from the choices in the following format: Answer: xxx.\n<image>\nABCD conforms a square. AB amounts to 3. Can you tell me the perimeter of ABCD?\nChoices:\nA.8*√(3)\nB.48\nC.12*√(2)/5\nD.12"
},
{
"from": "gpt",
"value": "Since ABCD is a square, the perimeter of ABCD is AB * 4 = 3 * 4 = 12. Answer: D"
}
] |
First perform reasoning, then select the answer from the choices in the following format: Answer: xxx.
<image>
|
{
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"path": "depth0_en/17/18_text.jpg"
}
|
Answer:
|
English
|
10
|
depth0
|
text_lite
|
multi_choice
|
[
{
"from": "human",
"value": "First perform reasoning, then select the answer from the choices in the following format: Answer: xxx.\n<image>\nABCD takes the form of a parallelogram. Angle ABC is equal to 30°, CB equals to 60. What is the measurement of DC in the shape ABCD?\nChoices:\nA.108\nB.120*√(3)\nC.300\nD.90"
},
{
"from": "gpt",
"value": "As AB is 90, and ABCD is a parallelogram with equal opposite sides, DC will also be 90. Answer: D"
}
] |
First perform reasoning, then select the answer from the choices in the following format: Answer: xxx.
<image>
|
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"path": "depth0_en/18/19_text.jpg"
}
|
Answer:
|
English
|
11
|
depth0
|
text_lite
|
multi_choice
|
[
{
"from": "human",
"value": "First perform reasoning, then select the answer from the choices in the following format: Answer: xxx.\n<image>\nArc CD is in the form of a semi-circle. AD is 1/2. Could you specify the length of CD in shape ABCD?\nChoices:\nA.π/2\nB.5*π/8\nC.π/8\nD.√(3)*π/8"
},
{
"from": "gpt",
"value": "CD, being opposite to AB, is also 1. Hence, the semicircle extending from C to D, using CD as its diameter, measures 1 * π/2 = π/2. Answer: A"
}
] |
First perform reasoning, then select the answer from the choices in the following format: Answer: xxx.
<image>
|
{
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"path": "depth0_en/19/20_text.jpg"
}
|
Answer:
|
English
|
12
|
depth0
|
text_lite
|
multi_choice
|
[
{
"from": "human",
"value": "First perform reasoning, then select the answer from the choices in the following format: Answer: xxx.\n<image>\nSquare ABCD encompasses an inscribed circle. AB is 55. How much is the perimeter of inscribed circle?\nChoices:\nA.275*√(2)*π/2\nB.55*π\nC.66*π\nD.55*√(2)*π/3"
},
{
"from": "gpt",
"value": "The circle inscribed in square ABCD has a diameter of AB = 55, so its circumference is 55 times π, resulting in 55*π. Answer: B"
}
] |
First perform reasoning, then select the answer from the choices in the following format: Answer: xxx.
<image>
|
{
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"path": "depth0_en/2/3_text.jpg"
}
|
Answer:
|
English
|
13
|
depth0
|
text_lite
|
multi_choice
|
[
{
"from": "human",
"value": "First perform reasoning, then select the answer from the choices in the following format: Answer: xxx.\n<image>\nCDE is classified as an equilateral triangle. AD totals 78. Could you specify the length of DE in shape ABCED?\nChoices:\nA.405/4\nB.81\nC.81*√(2)\nD.81/4"
},
{
"from": "gpt",
"value": "Given that AB is 81, the rectangle has opposite sides that are equal, so CD is also 81. Since CDE is an equilateral triangle, DE = CD = 81. Answer: B"
}
] |
First perform reasoning, then select the answer from the choices in the following format: Answer: xxx.
<image>
|
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"path": "depth0_en/20/21_text.jpg"
}
|
Answer:
|
English
|
14
|
depth0
|
text_lite
|
multi_choice
|
[
{
"from": "human",
"value": "First perform reasoning, then select the answer from the choices in the following format: Answer: xxx.\n<image>\nABCD is a square. AB is 3. What is the area of the entire shape ABCD?\nChoices:\nA.54\nB.9\nC.15*√(3)\nD.9/4"
},
{
"from": "gpt",
"value": "The area of square ABCD can be calculated as 3^2, which equals 9. Answer: B"
}
] |
First perform reasoning, then select the answer from the choices in the following format: Answer: xxx.
<image>
|
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"path": "depth0_en/21/22_text.jpg"
}
|
Answer:
|
English
|
15
|
depth0
|
text_lite
|
multi_choice
|
[
{
"from": "human",
"value": "First perform reasoning, then select the answer from the choices in the following format: Answer: xxx.\n<image>\nCDE is an equilateral triangle. AB equals to 32. What's the area of the entire shape ABCED?\nChoices:\nA.-640*√(6) + 4720*√(2)\nB.1888 - 256*√(3)\nC.2360 - 320*√(3)\nD.1888"
},
{
"from": "gpt",
"value": "CD is the opposite side of AB, so CD = AB = 32. CDE is an equilateral triangle, so the height of the triangle is CD * √(3)/2 = 16*√(3). The area of the pointing inwards triangle CDE is CD * height/2 = 256*√(3). The area of rectangle ABCD is 32*59 = 1888. Therefore, the total area of ABCED is 1888 - 256*√(3) = 1888 - 256*√(3). Answer: B"
}
] |
First perform reasoning, then select the answer from the choices in the following format: Answer: xxx.
<image>
|
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"path": "depth0_en/22/23_text.jpg"
}
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Answer:
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English
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16
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depth0
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text_lite
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multi_choice
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[
{
"from": "human",
"value": "First perform reasoning, then select the answer from the choices in the following format: Answer: xxx.\n<image>\nSide CD is prolonged into an equilateral triangle within the rectangle. AD is 3/2. What is the measurement of the total area of ABCED?\nChoices:\nA.9/5 - 3*√(3)/10\nB.6/5 - √(3)/5\nC.-3/2 + 3*√(3)\nD.3/2 - √(3)/4"
},
{
"from": "gpt",
"value": "Since CD is the opposite side of AB, CD = AB = 1. The triangle CDE is equilateral, so the height is CD * √(3)/2 = √(3)/2. The area of the inward-facing triangle CDE is CD * height/2 = √(3)/4. The area of the rectangle ABCD is 1 * 3/2 = 3/2. Thus, the total area of ABCED is 3/2 - √(3)/4 = 3/2 - √(3)/4. Answer: D"
}
] |
First perform reasoning, then select the answer from the choices in the following format: Answer: xxx.
<image>
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"path": "depth0_en/23/24_text.jpg"
}
|
Answer:
|
English
|
17
|
depth0
|
text_lite
|
multi_choice
|
[
{
"from": "human",
"value": "First perform reasoning, then select the answer from the choices in the following format: Answer: xxx.\n<image>\nABCD takes the form of a parallelogram. Angle ABC amounts to 45°, AD measures 19. In shape ABCD, what is the length of DC?\nChoices:\nA.13\nB.65*√(2)/2\nC.13/6\nD.247*√(2)/2"
},
{
"from": "gpt",
"value": "As AB is 13, and ABCD is a parallelogram with equal opposite sides, DC will also be 13. Answer: A"
}
] |
First perform reasoning, then select the answer from the choices in the following format: Answer: xxx.
<image>
|
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"path": "depth0_en/24/25_text.jpg"
}
|
Answer:
|
English
|
18
|
depth0
|
text_lite
|
multi_choice
|
[
{
"from": "human",
"value": "First perform reasoning, then select the answer from the choices in the following format: Answer: xxx.\n<image>\nABCD is a parallelogram. Angle ABC equals to 60°, CB equals to 4. Can you tell me the perimeter of ABCD?\nChoices:\nA.16\nB.40/3\nC.16*√(2)/5\nD.16*√(6)/3"
},
{
"from": "gpt",
"value": "Because ABCD is a parallelogram, opposite sides are equal, so the perimeter is (AB + CB) * 2 = (4 + 4) * 2 = 16. Answer: A"
}
] |
First perform reasoning, then select the answer from the choices in the following format: Answer: xxx.
<image>
|
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"path": "depth0_en/25/26_text.jpg"
}
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Answer:
|
English
|
19
|
depth0
|
text_lite
|
multi_choice
|
[
{
"from": "human",
"value": "First perform reasoning, then select the answer from the choices in the following format: Answer: xxx.\n<image>\nAB = 7. What is the total length of the perimeter of ABCD?\nChoices:\nA.√(6)*(4*√(3) + 7)\nB.6*√(3) + 21/2\nC.8*√(6)/3 + 14*√(2)/3\nD.8*√(3) + 14"
},
{
"from": "gpt",
"value": "The total length of the perimeter for ABCD is (AB+AD)*2, equating to (7+4*√(3))*2 = 8*√(3) + 14. Answer: D"
}
] |
First perform reasoning, then select the answer from the choices in the following format: Answer: xxx.
<image>
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"path": "depth0_en/26/27_text.jpg"
}
|
Answer:
|
English
|
20
|
depth0
|
text_lite
|
multi_choice
|
[
{
"from": "human",
"value": "First perform reasoning, then select the answer from the choices in the following format: Answer: xxx.\n<image>\nABCD conforms a parallelogram. AB is 3. Please provide the length of DC in shape ABCD.\nChoices:\nA.√(3)/2\nB.√(3)\nC.3\nD.√(2)"
},
{
"from": "gpt",
"value": "Given that AB measures 3. Because ABCD is a parallelogram, the opposite side, DC, is also 3. Answer: C"
}
] |
First perform reasoning, then select the answer from the choices in the following format: Answer: xxx.
<image>
|
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"path": "depth0_en/27/28_text.jpg"
}
|
Answer:
|
English
|
21
|
depth0
|
text_lite
|
multi_choice
|
[
{
"from": "human",
"value": "First perform reasoning, then select the answer from the choices in the following format: Answer: xxx.\n<image>\nABC is identified as a sector. AB is 13. How would you determine the perimeter of ABC?\nChoices:\nA.65*√(3)*(π + 8)/12\nB.13*π/4 + 26\nC.13*√(3)*(π + 8)/3\nD.13*√(3)*(π + 8)/16"
},
{
"from": "gpt",
"value": "The central angle of the sector measures 45° = π/4, and the radius AB is 13. Thus, the arc length AC equals 13 * π/4 = 13*π/4. Consequently, the perimeter is 13*2 + 13*π/4 = 13*π/4 + 26. Answer: B"
}
] |
First perform reasoning, then select the answer from the choices in the following format: Answer: xxx.
<image>
|
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"path": "depth0_en/28/29_text.jpg"
}
|
Answer:
|
English
|
22
|
depth0
|
text_lite
|
multi_choice
|
[
{
"from": "human",
"value": "First perform reasoning, then select the answer from the choices in the following format: Answer: xxx.\n<image>\nSquare ABCD has a circle inscribed. AB measures 11. Could you determine the area of the entire circle?\nChoices:\nA.363*π/10\nB.121*π/16\nC.121*π/4\nD.605*√(2)*π/8"
},
{
"from": "gpt",
"value": "The circle is inscribed in square ABCD, so its diameter is AB = 11, so its area is (11/2)^2 * π = 121*π/4. Answer: C"
}
] |
First perform reasoning, then select the answer from the choices in the following format: Answer: xxx.
<image>
|
{
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"path": "depth0_en/29/30_text.jpg"
}
|
Answer:
|
English
|
23
|
depth0
|
text_lite
|
multi_choice
|
[
{
"from": "human",
"value": "First perform reasoning, then select the answer from the choices in the following format: Answer: xxx.\n<image>\nABCD is geometrically a parallelogram. AB totals 81. Could you determine the area of the entire shape ABCD?\nChoices:\nA.1539*√(3)/2\nB.7695*√(2)/2\nC.7695*√(3)/2\nD.23085*√(6)/4"
},
{
"from": "gpt",
"value": "The area of parallelogram ABCD with angle ABC of 60° is AB * CB * sin(60°), equaling 81 * 95 * √(3)/2 = 7695*√(3)/2. Answer: C"
}
] |
First perform reasoning, then select the answer from the choices in the following format: Answer: xxx.
<image>
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"path": "depth0_en/3/4_text.jpg"
}
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Answer:
|
English
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24
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depth0
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text_lite
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multi_choice
|
[
{
"from": "human",
"value": "First perform reasoning, then select the answer from the choices in the following format: Answer: xxx.\n<image>\nSquare ABCD includes an inscribed circle. AB equals to 72. How much is the area of the entire circle?\nChoices:\nA.6480*π\nB.1296*π/5\nC.1296*√(3)*π/5\nD.1296*π"
},
{
"from": "gpt",
"value": "As the circle inscribed in square ABCD has a radius equal to half of AB = 36, it has an area of 36^2 * π = 1296*π. Answer: D"
}
] |
First perform reasoning, then select the answer from the choices in the following format: Answer: xxx.
<image>
|
{
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"path": "depth0_en/30/31_text.jpg"
}
|
Answer:
|
English
|
25
|
depth0
|
text_lite
|
open_ended
|
[
{
"from": "human",
"value": "First perform reasoning, then provide the answer in the following format: Answer: xxx.\n<image>\nCDE creates an equilateral triangle. AB = 80. In shape ABCED, what is the length of DE?"
},
{
"from": "gpt",
"value": "As AB is 80, the rectangle has equal opposite edges, so CD is also 80. Given that CDE is an equilateral triangle, DE = CD = 80. Answer: 80"
}
] |
First perform reasoning, then provide the answer in the following format: Answer: xxx.
<image>
|
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"path": "depth0_en/31/32_text.jpg"
}
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Answer:
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English
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26
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depth0
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text_lite
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open_ended
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[
{
"from": "human",
"value": "First perform reasoning, then provide the answer in the following format: Answer: xxx.\n<image>\nAngle ACB is equal to 45°. What's the area of the entire shape ABC?"
},
{
"from": "gpt",
"value": "ABC is right triangle. The area of the triangle is AB * BC / 2 = 648. Answer: 648"
}
] |
First perform reasoning, then provide the answer in the following format: Answer: xxx.
<image>
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"path": "depth0_en/32/33_text.jpg"
}
|
Answer:
|
English
|
27
|
depth0
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text_lite
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open_ended
|
[
{
"from": "human",
"value": "First perform reasoning, then provide the answer in the following format: Answer: xxx.\n<image>\nABC forms a sector. Angle CBA measures 120°. Can you calculate the perimeter of ABC?"
},
{
"from": "gpt",
"value": "The central angle of the sector measures 120° which equals 2*π/3, with the radius AB being 72. Therefore, the arc length AC equals 72 * 2*π/3 = 48*π. Hence, the perimeter is 72*2 + 48*π = 144 + 48*π. Answer: 144 + 48*π"
}
] |
First perform reasoning, then provide the answer in the following format: Answer: xxx.
<image>
|
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"path": "depth0_en/33/34_text.jpg"
}
|
Answer:
|
English
|
28
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depth0
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text_lite
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open_ended
|
[
{
"from": "human",
"value": "First perform reasoning, then provide the answer in the following format: Answer: xxx.\n<image>\nCDE is shaped as an equilateral triangle. AB equals to 99. What is the overall perimeter of ABCED?"
},
{
"from": "gpt",
"value": "The rectangle ABCD has CD as the opposite side of AB, meaning CD = 99. Since the triangle CDE is equilateral, CE = ED = 99. Therefore, the perimeter is AB + AD + BC + ED + CE = 99 + 99 + 99 + 99 + 99 = 495. Answer: 495"
}
] |
First perform reasoning, then provide the answer in the following format: Answer: xxx.
<image>
|
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"path": "depth0_en/34/35_text.jpg"
}
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Answer:
|
English
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29
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depth0
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text_lite
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open_ended
|
[
{
"from": "human",
"value": "First perform reasoning, then provide the answer in the following format: Answer: xxx.\n<image>\nSide CD develops into a semi-circle inside the rectangle. AD totals √(3). How do you find the area of the entire shape ABCD?"
},
{
"from": "gpt",
"value": "Rectangle ABCD has an area calculated as AB * AD, or 1 * √(3), which equals √(3). The semicircle with CD as the diameter has an area of (AB/2)^2 * π/2, equaling π/8. Subtracting these, the total area is √(3) - π/8 = -π/8 + √(3). Answer: -π/8 + √(3)"
}
] |
First perform reasoning, then provide the answer in the following format: Answer: xxx.
<image>
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"path": "depth0_en/35/36_text.jpg"
}
|
Answer:
|
English
|
30
|
depth0
|
text_lite
|
open_ended
|
[
{
"from": "human",
"value": "First perform reasoning, then provide the answer in the following format: Answer: xxx.\n<image>\nSide CD continues into an equilateral triangle inside the rectangle. AB span 1. What is the total boundary length of ABCED?"
},
{
"from": "gpt",
"value": "The shape ABCD is a rectangle. Because CD is opposite to AB, CD is 1. The triangle CDE is equilateral, so CE and ED are both 1. Thus, the perimeter is AB + AD + BC + ED + CE = 1 + 3/2 + 3/2 + 1 + 1 = 6. Answer: 6"
}
] |
First perform reasoning, then provide the answer in the following format: Answer: xxx.
<image>
|
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"path": "depth0_en/36/37_text.jpg"
}
|
Answer:
|
English
|
31
|
depth0
|
text_lite
|
open_ended
|
[
{
"from": "human",
"value": "First perform reasoning, then provide the answer in the following format: Answer: xxx.\n<image>\nAB is equal to 30. What would the area of the entire shape ABC be?"
},
{
"from": "gpt",
"value": "ABC is a right-angled triangle. The area is calculated as AB * BC / 2 = 450. Answer: 450"
}
] |
First perform reasoning, then provide the answer in the following format: Answer: xxx.
<image>
|
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"path": "depth0_en/37/38_text.jpg"
}
|
Answer:
|
English
|
32
|
depth0
|
text_lite
|
open_ended
|
[
{
"from": "human",
"value": "First perform reasoning, then provide the answer in the following format: Answer: xxx.\n<image>\nSquare ABCD has a circle inscribed within it. AB = 56. How long is AD in shape ABCD?"
},
{
"from": "gpt",
"value": "AB equals 56. As ABCD is a square, all its sides are of equal length. Thus, AD = AB = 56. Answer: 56"
}
] |
First perform reasoning, then provide the answer in the following format: Answer: xxx.
<image>
|
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"path": "depth0_en/38/39_text.jpg"
}
|
Answer:
|
English
|
33
|
depth0
|
text_lite
|
open_ended
|
[
{
"from": "human",
"value": "First perform reasoning, then provide the answer in the following format: Answer: xxx.\n<image>\nAB is equal to 2. What is the total perimeter measurement of ABC?"
},
{
"from": "gpt",
"value": "Since AB = 2 and angle ACB is 30°, the adjacent side BC is AB / tan(30°) = 2 / (√(3)/3) = 2*√(3). The hypotenuse AC is AB / sin(30°) = 2 / (1/2) = 4, giving the perimeter as AB + BC + AC = 2*√(3) + 6. Answer: 2*√(3) + 6"
}
] |
First perform reasoning, then provide the answer in the following format: Answer: xxx.
<image>
|
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"path": "depth0_en/39/40_text.jpg"
}
|
Answer:
|
English
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34
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depth0
|
text_lite
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open_ended
|
[
{
"from": "human",
"value": "First perform reasoning, then provide the answer in the following format: Answer: xxx.\n<image>\nABCD is a parallelogram. AB = 77. In the shape ABCD, what is the measurement of DC?"
},
{
"from": "gpt",
"value": "Given that AB is 77. Since ABCD is a parallelogram, opposite sides are equal. Therefore, DC is also 77. Answer: 77"
}
] |
First perform reasoning, then provide the answer in the following format: Answer: xxx.
<image>
|
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"path": "depth0_en/4/5_text.jpg"
}
|
Answer:
|
English
|
35
|
depth0
|
text_lite
|
open_ended
|
[
{
"from": "human",
"value": "First perform reasoning, then provide the answer in the following format: Answer: xxx.\n<image>\nSquare ABCD contains a circle that is inscribed. AB equals to 42. How much is the area of the entire circle?"
},
{
"from": "gpt",
"value": "Since the circle inscribed in square ABCD has a radius of AB/2 = 21, its area is 21^2 * π = 441*π. Answer: 441*π"
}
] |
First perform reasoning, then provide the answer in the following format: Answer: xxx.
<image>
|
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"path": "depth0_en/40/41_text.jpg"
}
|
Answer:
|
English
|
36
|
depth0
|
text_lite
|
open_ended
|
[
{
"from": "human",
"value": "First perform reasoning, then provide the answer in the following format: Answer: xxx.\n<image>\nSide CD is extended to form an equilateral triangle inside the rectangle. AD is 65. What is the full perimeter of ABCED?"
},
{
"from": "gpt",
"value": "The shape ABCD is a rectangle. Because CD is opposite to AB, CD is 39. The triangle CDE is equilateral, so CE and ED are both 39. Thus, the perimeter is AB + AD + BC + ED + CE = 39 + 65 + 65 + 39 + 39 = 247. Answer: 247"
}
] |
First perform reasoning, then provide the answer in the following format: Answer: xxx.
<image>
|
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"path": "depth0_en/41/42_text.jpg"
}
|
Answer:
|
English
|
37
|
depth0
|
text_lite
|
open_ended
|
[
{
"from": "human",
"value": "First perform reasoning, then provide the answer in the following format: Answer: xxx.\n<image>\nSquare ABCD has an inscribed circle. AB span 2. What is the measurement of the perimeter of inscribed circle?"
},
{
"from": "gpt",
"value": "The circle is inscribed within square ABCD, giving it a diameter of AB = 2. Therefore, the circumference of the circle is 2 * π = 2*π. Answer: 2*π"
}
] |
First perform reasoning, then provide the answer in the following format: Answer: xxx.
<image>
|
{
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"path": "depth0_en/42/43_text.jpg"
}
|
Answer:
|
English
|
38
|
depth0
|
text_lite
|
open_ended
|
[
{
"from": "human",
"value": "First perform reasoning, then provide the answer in the following format: Answer: xxx.\n<image>\nCB equals to 4. In the shape ABCD, what is the measurement of DC?"
},
{
"from": "gpt",
"value": "Since AB is 2 and ABCD is a rectangle, its opposite sides are equal. Hence, DC is also 2. Answer: 2"
}
] |
First perform reasoning, then provide the answer in the following format: Answer: xxx.
<image>
|
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"path": "depth0_en/43/44_text.jpg"
}
|
Answer:
|
English
|
39
|
depth0
|
text_lite
|
open_ended
|
[
{
"from": "human",
"value": "First perform reasoning, then provide the answer in the following format: Answer: xxx.\n<image>\nArc CD constitutes a semi-circle. AD is 42. How much is the perimeter of ABCD?"
},
{
"from": "gpt",
"value": "CD is the side opposite AB, so CD is also 50. The semicircle extending from C to D has CD as its diameter, with a length of 50 * π/2 = 25*π. The shape's total perimeter is AB + AD + BC + the semicircle CD, amounting to 50 + 42 + 42 + 25*π = 25*π + 134. Answer: 25*π + 134"
}
] |
First perform reasoning, then provide the answer in the following format: Answer: xxx.
<image>
|
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"path": "depth0_en/44/45_text.jpg"
}
|
Answer:
|
English
|
40
|
depth0
|
text_lite
|
open_ended
|
[
{
"from": "human",
"value": "First perform reasoning, then provide the answer in the following format: Answer: xxx.\n<image>\nABCD conforms a square. AB amounts to 96. What is the area of the entire shape ABCD?"
},
{
"from": "gpt",
"value": "The square ABCD has an area of 96^2, which is 9216. Answer: 9216"
}
] |
First perform reasoning, then provide the answer in the following format: Answer: xxx.
<image>
|
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"path": "depth0_en/45/46_text.jpg"
}
|
Answer:
|
English
|
41
|
depth0
|
text_lite
|
open_ended
|
[
{
"from": "human",
"value": "First perform reasoning, then provide the answer in the following format: Answer: xxx.\n<image>\nCDE is shaped as an equilateral triangle. AB is 44. How long is EC in shape ABCED?"
},
{
"from": "gpt",
"value": "Given AB is 44, the rectangle has equal opposite sides, making CD also 44. As CDE forms an equilateral triangle, EC = CD = 44. Answer: 44"
}
] |
First perform reasoning, then provide the answer in the following format: Answer: xxx.
<image>
|
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"path": "depth0_en/46/47_text.jpg"
}
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Answer:
|
English
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42
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depth0
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text_lite
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open_ended
|
[
{
"from": "human",
"value": "First perform reasoning, then provide the answer in the following format: Answer: xxx.\n<image>\nAngle ACB is equal to 30°. What is the overall perimeter of ABC?"
},
{
"from": "gpt",
"value": "Because AB = 27 and angle ACB is 30°, we have BC = AB / tan(30°) = 27 / (√(3)/3) = 27*√(3). The hypotenuse AC is AB / sin(30°) = 27 / (1/2) = 54, making the perimeter AB + BC + AC = 27*√(3) + 81. Answer: 27*√(3) + 81"
}
] |
First perform reasoning, then provide the answer in the following format: Answer: xxx.
<image>
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"path": "depth0_en/47/48_text.jpg"
}
|
Answer:
|
English
|
43
|
depth0
|
text_lite
|
open_ended
|
[
{
"from": "human",
"value": "First perform reasoning, then provide the answer in the following format: Answer: xxx.\n<image>\nABCD is geometrically a parallelogram. AB totals 52. What is the full area of the shape ABCD?"
},
{
"from": "gpt",
"value": "Parallelogram ABCD with an angle ABC of 60° has an area of AB * CB * sin(60°), which is 52 * 96 * √(3)/2 = 2496*√(3). Answer: 2496*√(3)"
}
] |
First perform reasoning, then provide the answer in the following format: Answer: xxx.
<image>
|
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"path": "depth0_en/48/49_text.jpg"
}
|
Answer:
|
English
|
44
|
depth0
|
text_lite
|
open_ended
|
[
{
"from": "human",
"value": "First perform reasoning, then provide the answer in the following format: Answer: xxx.\n<image>\nABCD conforms a parallelogram. AB equals to 12. How long is DC in shape ABCD?"
},
{
"from": "gpt",
"value": "Since AB is 12, and ABCD is a parallelogram with equal opposite sides, DC is also 12. Answer: 12"
}
] |
First perform reasoning, then provide the answer in the following format: Answer: xxx.
<image>
|
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"path": "depth0_en/49/50_text.jpg"
}
|
Answer:
|
English
|
45
|
depth0
|
text_lite
|
open_ended
|
[
{
"from": "human",
"value": "First perform reasoning, then provide the answer in the following format: Answer: xxx.\n<image>\nSide CD is extended into a semi-circular shape inside the rectangle. AD span 4. What is the area of the entire shape ABCD?"
},
{
"from": "gpt",
"value": "The area of rectangle ABCD equals AB * AD, which is 2 * 4 = 8. The semicircle with CD as its diameter has an area of (AB/2)^2 * π/2 = π/2. Subtracting the semicircle's area from the rectangle's area gives us 8 - π/2 = 8 - π/2. Answer: 8 - π/2"
}
] |
First perform reasoning, then provide the answer in the following format: Answer: xxx.
<image>
|
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"path": "depth0_en/5/6_text.jpg"
}
|
Answer:
|
English
|
46
|
depth0
|
text_lite
|
open_ended
|
[
{
"from": "human",
"value": "First perform reasoning, then provide the answer in the following format: Answer: xxx.\n<image>\nSquare ABCD has an inner inscribed circle. AB equals to 2. What is the perimeter of inscribed circle?"
},
{
"from": "gpt",
"value": "Since the circle inscribed in square ABCD has a diameter of AB = 2, its circumference is 2 * π = 2*π. Answer: 2*π"
}
] |
First perform reasoning, then provide the answer in the following format: Answer: xxx.
<image>
|
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"path": "depth0_en/50/51_text.jpg"
}
|
Answer:
|
English
|
47
|
depth0
|
text_lite
|
open_ended
|
[
{
"from": "human",
"value": "First perform reasoning, then provide the answer in the following format: Answer: xxx.\n<image>\nABCD is geometrically a parallelogram. AB totals 3. What is the total area of shape ABCD?"
},
{
"from": "gpt",
"value": "Parallelogram ABCD has a angle ABC of 45°, so area is AB * AD * sin(45°) = 3 * 3*√(2) * √(2)/2 = 9. Answer: 9"
}
] |
First perform reasoning, then provide the answer in the following format: Answer: xxx.
<image>
|
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"path": "depth0_en/51/52_text.jpg"
}
|
Answer:
|
English
|
48
|
depth0
|
text_lite
|
open_ended
|
[
{
"from": "human",
"value": "First perform reasoning, then provide the answer in the following format: Answer: xxx.\n<image>\nSide CD extends and forms a semi-circle inside the rectangle. AD totals 38. What is the perimeter length of ABCD?"
},
{
"from": "gpt",
"value": "CD is opposite to AB, so CD is also 24. The semicircle from C to D has CD as its diameter, with a length of 24 * π/2 = 12*π. The total perimeter of the shape is AB + AD + BC + the semicircle CD, which equals 24 + 38 + 38 + 12*π = 12*π + 100. Answer: 12*π + 100"
}
] |
First perform reasoning, then provide the answer in the following format: Answer: xxx.
<image>
|
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"path": "depth0_en/52/53_text.jpg"
}
|
Answer:
|
English
|
49
|
depth0
|
text_lite
|
open_ended
|
[
{
"from": "human",
"value": "First perform reasoning, then provide the answer in the following format: Answer: xxx.\n<image>\nABC is an isosceles triangle, with AB equalling BC. Angle CBA = 120°. What are the measures of angle BAC and angle ACB in the isosceles triangle ABC?"
},
{
"from": "gpt",
"value": "As ABC is an isosceles triangle with vertex angle B of 120°, it follows that angle BAC and angle ACB are (180° - 120°) / 2 = 30°. Answer: 30"
}
] |
First perform reasoning, then provide the answer in the following format: Answer: xxx.
<image>
|
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"path": "depth0_en/53/54_text.jpg"
}
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Answer:
|
English
|
50
|
depth1
|
text_lite
|
multi_choice
|
[
{
"from": "human",
"value": "First perform reasoning, then select the answer from the choices in the following format: Answer: xxx.\n<image>\nSide CD growing into an equilateral triangle outside the rectangle. Square DEFG contains an inscribed circle. AB span 1. In the shape DEFG, what is the measurement of FE?\nChoices:\nA.√(3)/4\nB.5/6\nC.1\nD.5/3"
},
{
"from": "gpt",
"value": "Given that AB is 1, rectangle has equal oppsite edges, so CD is also 1. Since CDE is a equilateral triangle, DE = CD = 1. As DEFG is a square with all sides of equal length, FE = DE = 1. Answer: C"
}
] |
First perform reasoning, then select the answer from the choices in the following format: Answer: xxx.
<image>
|
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"path": "depth1_en/0/1_text.jpg"
}
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Answer:
|
English
|
51
|
depth1
|
text_lite
|
multi_choice
|
[
{
"from": "human",
"value": "First perform reasoning, then select the answer from the choices in the following format: Answer: xxx.\n<image>\nACDE is geometrically a square. Angle ACB amounts to 30°. What is the length of DC in shape ACDE?\nChoices:\nA.24/5\nB.4\nC.12\nD.12*√(2)"
},
{
"from": "gpt",
"value": "With AB being 6 and an angle of 30° at C, AC is AB / sin(30°), which equals 6 / (1/2) = 12. As ACDE is a square with all sides of equal length, DC = AC = 12. Answer: C"
}
] |
First perform reasoning, then select the answer from the choices in the following format: Answer: xxx.
<image>
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"path": "depth1_en/1/2_text.jpg"
}
|
Answer:
|
English
|
52
|
depth1
|
text_lite
|
multi_choice
|
[
{
"from": "human",
"value": "First perform reasoning, then select the answer from the choices in the following format: Answer: xxx.\n<image>\nSide CD turns into an equilateral triangle. Square DEFG includes a circle inscribed within. AB amounts to 63. Can you tell me the length of FE in shape DEFG?\nChoices:\nA.21*√(2)/2\nB.63/5\nC.63\nD.189*√(2)"
},
{
"from": "gpt",
"value": "As AB is 63, the rectangle has equal opposite edges, so CD is also 63. Given that CDE is an equilateral triangle, DE = CD = 63. Because DEFG is a square, all sides are the same length. Hence, FE = DE = 63. Answer: C"
}
] |
First perform reasoning, then select the answer from the choices in the following format: Answer: xxx.
<image>
|
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"path": "depth1_en/10/11_text.jpg"
}
|
Answer:
|
English
|
53
|
depth1
|
text_lite
|
multi_choice
|
[
{
"from": "human",
"value": "First perform reasoning, then select the answer from the choices in the following format: Answer: xxx.\n<image>\nABCD conforms a square. EFG is shaped as an equilateral triangle. AB totals 54. What is the area size of the entire shape CBEGF?\nChoices:\nA.-243*√(6) + 1584*√(2)\nB.19008 - 2916*√(3)\nC.4752 - 729*√(3)\nD.-729 + 1584*√(3)"
},
{
"from": "gpt",
"value": "AB is 54. Since ABCD is a square and all four sides are equal, CB is also AB = 54. Because EF is the opposite side of CB, it follows that EF = CB = 54. The triangle EFG is equilateral, so its height is EF * √(3)/2 = 27*√(3). The area of the inward-facing triangle EFG is EF * height/2 = 729*√(3). The area of the rectangle CBEF is 54 * 88 = 4752. Therefore, the total area of CBEGF is 4752 - 729*√(3) = 4752 - 729*√(3). Answer: C"
}
] |
First perform reasoning, then select the answer from the choices in the following format: Answer: xxx.
<image>
|
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"path": "depth1_en/11/12_text.jpg"
}
|
Answer:
|
English
|
54
|
depth1
|
text_lite
|
multi_choice
|
[
{
"from": "human",
"value": "First perform reasoning, then select the answer from the choices in the following format: Answer: xxx.\n<image>\nABC is identified as a sector. AB equals to 7. What is the area size of the entire shape CBDE?\nChoices:\nA.196*√(3)\nB.196*√(3)/3\nC.98\nD.98*√(2)"
},
{
"from": "gpt",
"value": "The length of AB is 7. Since the sector's radius does not change, BC is 7. The area of rectangle CBDE = CB*DB = 7*14 = 98. Answer: C"
}
] |
First perform reasoning, then select the answer from the choices in the following format: Answer: xxx.
<image>
|
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"path": "depth1_en/12/13_text.jpg"
}
|
Answer:
|
English
|
55
|
depth1
|
text_lite
|
multi_choice
|
[
{
"from": "human",
"value": "First perform reasoning, then select the answer from the choices in the following format: Answer: xxx.\n<image>\nSide DE extending into an equilateral triangle beyond the rectangle. AB totals 60, Angle ACB is equal to 30°. What's the area of the entire shape ACDFE?\nChoices:\nA.1440*√(3) + 2160*√(2)\nB.3600*√(3) + 5400*√(2)\nC.900*√(6) + 2700\nD.2880*√(3) + 4320*√(2)"
},
{
"from": "gpt",
"value": "Since AB is 60 and the angle at C is 30°, the length of AC is AB / sin(30°) = 60 / (1/2) = 120. DE being the side opposite AC means that DE = AC = 120. The height of the equilateral triangle DEF is DE * √(3)/2 = 60*√(3). The area of triangle DEF is DE * height/2 = 3600*√(3). The area of rectangle ACDE is 120 * 45*√(2) = 5400*√(2). Therefore, the total area of ACDFE is 3600*√(3) + 5400*√(2) = 3600*√(3) + 5400*√(2). Answer: B"
}
] |
First perform reasoning, then select the answer from the choices in the following format: Answer: xxx.
<image>
|
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"path": "depth1_en/13/14_text.jpg"
}
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Answer:
|
English
|
56
|
depth1
|
text_lite
|
multi_choice
|
[
{
"from": "human",
"value": "First perform reasoning, then select the answer from the choices in the following format: Answer: xxx.\n<image>\nSide EF arcs into a semi-circle outside. AB amounts to 72. How can we determine the area of the entire shape DCEF?\nChoices:\nA.648*√(3)*(π + 7*√(2))/5\nB.648*√(2)*π + 9072\nC.648*π + 4536*√(2)\nD.1296*π/5 + 9072*√(2)/5"
},
{
"from": "gpt",
"value": "Considering that AB is 72. Since ABCD is a rectangle, its opposite sides are equal. Hence, DC is also 72. Rectangle DCEF has an area of DC * DF, or 72 * 63*√(2), which equals 4536*√(2). The semicircle with diameter EF has an area calculated by (DC/2)^2 * π/2 = 648*π. The combined area is 4536*√(2) + 648*π = 648*π + 4536*√(2). Answer: C"
}
] |
First perform reasoning, then select the answer from the choices in the following format: Answer: xxx.
<image>
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"path": "depth1_en/14/15_text.jpg"
}
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Answer:
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English
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57
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depth1
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text_lite
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multi_choice
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[
{
"from": "human",
"value": "First perform reasoning, then select the answer from the choices in the following format: Answer: xxx.\n<image>\nABCD is identified as a parallelogram. Side EF projecting into an equilateral triangle beyond the rectangle. AB span 84. What is the overall area measurement of the shape DCEGF?\nChoices:\nA.8820*√(3)\nB.15876*√(3)\nC.5292*√(3)\nD.1764*√(3)"
},
{
"from": "gpt",
"value": "Given that AB is 84. Since ABCD is a parallelogram, opposite sides are equal. Therefore, DC is also 84. Given that EF is the opposite side of DC, we know EF = DC = 84. The height of the equilateral triangle EFG is EF * √(3)/2 = 42*√(3). The area of triangle EFG is EF * height/2 = 1764*√(3). The rectangle DCEF has an area of 84 * 42*√(3) = 3528*√(3). Thus, the total area of DCEGF is 1764*√(3) + 3528*√(3) = 5292*√(3). Answer: C"
}
] |
First perform reasoning, then select the answer from the choices in the following format: Answer: xxx.
<image>
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"path": "depth1_en/15/16_text.jpg"
}
|
Answer:
|
English
|
58
|
depth1
|
text_lite
|
multi_choice
|
[
{
"from": "human",
"value": "First perform reasoning, then select the answer from the choices in the following format: Answer: xxx.\n<image>\nAB equals to 48, DB is equal to 35. Could you specify the length of ED in shape CBDE?\nChoices:\nA.8*√(3)\nB.16*√(6)\nC.48\nD.32"
},
{
"from": "gpt",
"value": "With AB = 48 and an angle of 45° at C, BC is AB / tan(45°), which equals 48 / 1 = 48. As CBDE is a rectangle, opposite sides are equal. Therefore, ED is also 48. Answer: C"
}
] |
First perform reasoning, then select the answer from the choices in the following format: Answer: xxx.
<image>
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"path": "depth1_en/16/17_text.jpg"
}
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Answer:
|
English
|
59
|
depth1
|
text_lite
|
multi_choice
|
[
{
"from": "human",
"value": "First perform reasoning, then select the answer from the choices in the following format: Answer: xxx.\n<image>\nABCD is a square. ADE is an isosceles triangle, with AD equalling DE. AB is equal to 96. How large are angle DAE and angle AED in the isosceles triangle ADE?\nChoices:\nA.240\nB.40\nC.45\nD.60"
},
{
"from": "gpt",
"value": "AB equals 96. As ABCD is a square, all its sides are of equal length. Thus, AD = AB = 96. Since ADE is an isosceles triangle with vertex angle D of 60°, angle DAE and angle AED are (180° - 60°) / 2 = 60°. Answer: D"
}
] |
First perform reasoning, then select the answer from the choices in the following format: Answer: xxx.
<image>
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"path": "depth1_en/17/18_text.jpg"
}
|
Answer:
|
English
|
60
|
depth1
|
text_lite
|
multi_choice
|
[
{
"from": "human",
"value": "First perform reasoning, then select the answer from the choices in the following format: Answer: xxx.\n<image>\nDCE is an isosceles triangle where the lengths of DC and CE are equal. Angle ECD amounts to 120°. In shape DCE, how long is EC?\nChoices:\nA.36*√(3)/5\nB.90\nC.45\nD.36"
},
{
"from": "gpt",
"value": "Given that AB is 36. As ABCD is a rectangle, the opposite sides are the same. Hence, DC is also 36. Given that DCE is an isosceles triangle, CE is also 36. Answer: D"
}
] |
First perform reasoning, then select the answer from the choices in the following format: Answer: xxx.
<image>
|
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"path": "depth1_en/18/19_text.jpg"
}
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Answer:
|
English
|
61
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depth1
|
text_lite
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multi_choice
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[
{
"from": "human",
"value": "First perform reasoning, then select the answer from the choices in the following format: Answer: xxx.\n<image>\nABC takes the form of a sector. Side DE is extended to form an equilateral triangle inside the rectangle. CE = 69. How do you find the area of the entire shape CBDFE?\nChoices:\nA.2484 - 324*√(3)\nB.7452 - 972*√(3)\nC.π/4\nD.9*π"
},
{
"from": "gpt",
"value": "AB is 36. Because the sector's radius is constant, BC is 36. Given that DE is opposite to CB, it follows that DE = CB = 36. The height of the equilateral triangle DEF is DE * √(3)/2 = 18*√(3). The area of the inward-pointing triangle DEF is DE * height/2 = 324*√(3). The area of the rectangle CBDE is 36 * 69 = 2484. Therefore, the total area of CBDFE is 2484 - 324*√(3) = 2484 - 324*√(3). Answer: A"
}
] |
First perform reasoning, then select the answer from the choices in the following format: Answer: xxx.
<image>
|
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"path": "depth1_en/19/20_text.jpg"
}
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Answer:
|
English
|
62
|
depth1
|
text_lite
|
multi_choice
|
[
{
"from": "human",
"value": "First perform reasoning, then select the answer from the choices in the following format: Answer: xxx.\n<image>\nEC amounts to 9*√(2). In the shape DCEF, what is the measurement of FE?\nChoices:\nA.12\nB.20*√(3)\nC.30*√(2)\nD.18*√(2)"
},
{
"from": "gpt",
"value": "Given that AB is 12. Since ABCD is a rectangle, the opposite sides must be equal. Thus, DC is also 12. Since DCEF is a rectangle, its opposite sides are equal. Thus, FE is also 12. Answer: A"
}
] |
First perform reasoning, then select the answer from the choices in the following format: Answer: xxx.
<image>
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"path": "depth1_en/2/3_text.jpg"
}
|
Answer:
|
English
|
63
|
depth1
|
text_lite
|
multi_choice
|
[
{
"from": "human",
"value": "First perform reasoning, then select the answer from the choices in the following format: Answer: xxx.\n<image>\nCDE defines an equilateral triangle. Side FG forms an inward semi-circle within the rectangle. AB equals to 13. What is the overall area of the shape ECFG?\nChoices:\nA.13*√(2)*(56 - 13*π)/40\nB.182/5 - 169*π/20\nC.√(2)*(273 - 507*π/8)\nD.91 - 169*π/8"
},
{
"from": "gpt",
"value": "As AB is 13, the rectangle has equal opposite edges, so CD is also 13. Given that CDE is an equilateral triangle, EC = CD = 13. The rectangle ECFG has an area of EC * EG = 13 * 7, giving 91. For the semicircle with FG as the diameter, the area is (EC/2)^2 * π/2 = 169*π/8. The combined area is then 91 - 169*π/8 = 91 - 169*π/8. Answer: D"
}
] |
First perform reasoning, then select the answer from the choices in the following format: Answer: xxx.
<image>
|
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"path": "depth1_en/20/21_text.jpg"
}
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Answer:
|
English
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64
|
depth1
|
text_lite
|
multi_choice
|
[
{
"from": "human",
"value": "First perform reasoning, then select the answer from the choices in the following format: Answer: xxx.\n<image>\nABCD is identified as a parallelogram. DCE is an isosceles triangle in which DC equals CE in length. Angle ECD = 120°. What is the area of the entire shape DCE?\nChoices:\nA.√(3)/3\nB.√(3)/4\nC.√(3)/24\nD.√(6)/12"
},
{
"from": "gpt",
"value": "Given that AB is 1, and because ABCD is a parallelogram, it means DC will also be 1. Given that DCE is an isosceles triangle with a vertex angle of 120°, the area is DC * CE * sin(120°) / 2 = √(3)/4. Answer: B"
}
] |
First perform reasoning, then select the answer from the choices in the following format: Answer: xxx.
<image>
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"path": "depth1_en/21/22_text.jpg"
}
|
Answer:
|
English
|
65
|
depth1
|
text_lite
|
multi_choice
|
[
{
"from": "human",
"value": "First perform reasoning, then select the answer from the choices in the following format: Answer: xxx.\n<image>\nABC is an isosceles triangle where the length of AB equals the length of BC. AB span 2. How can we determine the area of the entire shape CBDE?\nChoices:\nA.12/5\nB.4*√(3)/3\nC.2\nD.5"
},
{
"from": "gpt",
"value": "Given that AB is 2, ABC being an isosceles triangle means that BC is also 2. The area of rectangle CBDE = CB*CE = 2*1 = 2. Answer: C"
}
] |
First perform reasoning, then select the answer from the choices in the following format: Answer: xxx.
<image>
|
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"path": "depth1_en/22/23_text.jpg"
}
|
Answer:
|
English
|
66
|
depth1
|
text_lite
|
multi_choice
|
[
{
"from": "human",
"value": "First perform reasoning, then select the answer from the choices in the following format: Answer: xxx.\n<image>\nABC is an isosceles triangle in which AB equals BC in length. DEF is geometrically an equilateral triangle. AB = 1. How much is the area of the entire shape CBDFE?\nChoices:\nA.1/2 - √(3)/8\nB.1/6 - √(3)/24\nC.4/3 - √(3)/3\nD.1 - √(3)/4"
},
{
"from": "gpt",
"value": "AB measures 1. Because ABC is an isosceles triangle, BC is also 1. DE, being the opposite side of CB, means DE = CB = 1. The equilateral triangle DEF has a height of DE * √(3)/2 = √(3)/2. The area of the inward-pointing triangle DEF is DE * height/2 = √(3)/4. The area of the rectangle CBDE is 1 * 1 = 1. Therefore, the total area of CBDFE is 1 - √(3)/4 = 1 - √(3)/4. Answer: D"
}
] |
First perform reasoning, then select the answer from the choices in the following format: Answer: xxx.
<image>
|
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"path": "depth1_en/23/24_text.jpg"
}
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Answer:
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English
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67
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depth1
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text_lite
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multi_choice
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[
{
"from": "human",
"value": "First perform reasoning, then select the answer from the choices in the following format: Answer: xxx.\n<image>\nABCD conforms a square. Square ADEF includes an inscribed circle. AB = 72. What is the overall perimeter of inscribed circle?\nChoices:\nA.72*π\nB.36*√(2)*π\nC.72*π/5\nD.72"
},
{
"from": "gpt",
"value": "AB measures 72. As ABCD is a square, all sides are identical. Therefore, AD = AB = 72. The circle is inscribed within square ADEF, giving it a diameter of AD = 72. Therefore, the circumference of the circle is 72 * π = 72*π. Answer: A"
}
] |
First perform reasoning, then select the answer from the choices in the following format: Answer: xxx.
<image>
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"path": "depth1_en/24/25_text.jpg"
}
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Answer:
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English
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68
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depth1
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text_lite
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multi_choice
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[
{
"from": "human",
"value": "First perform reasoning, then select the answer from the choices in the following format: Answer: xxx.\n<image>\nACDE conforms a square. Angle ACB totals 45°. In shape ACDE, what is the length of ED?\nChoices:\nA.455*√(2)/6\nB.91*√(2)\nC.8281/2\nD.546*√(2)"
},
{
"from": "gpt",
"value": "As AB = 91 and angle ACB = 45°, AC is calculated as AB / sin(45°) = 91 / (√(2)/2) = 91*√(2). As ACDE is a square, all sides are identical. Therefore, ED = AC = 91*√(2). Answer: B"
}
] |
First perform reasoning, then select the answer from the choices in the following format: Answer: xxx.
<image>
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"path": "depth1_en/25/26_text.jpg"
}
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Answer:
|
English
|
69
|
depth1
|
text_lite
|
multi_choice
|
[
{
"from": "human",
"value": "First perform reasoning, then select the answer from the choices in the following format: Answer: xxx.\n<image>\nABC is an isosceles triangle where the length of AB equals the length of BC. CBDE conforms a square. AB equals to 12. In the shape CBDE, what is the measurement of ED?\nChoices:\nA.24\nB.8*√(3)\nC.12*√(2)\nD.12"
},
{
"from": "gpt",
"value": "AB equals 12. As ABC is an isosceles triangle, BC is also 12. Given that CBDE is a square and all sides are equal, ED = CB = 12. Answer: D"
}
] |
First perform reasoning, then select the answer from the choices in the following format: Answer: xxx.
<image>
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"path": "depth1_en/26/27_text.jpg"
}
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Answer:
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English
|
70
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depth1
|
text_lite
|
multi_choice
|
[
{
"from": "human",
"value": "First perform reasoning, then select the answer from the choices in the following format: Answer: xxx.\n<image>\nACDE is geometrically a square. AB span 48. How long is the perimeter of ACDE?\nChoices:\nA.64\nB.32*√(6)\nC.128*√(3)\nD.96"
},
{
"from": "gpt",
"value": "As AB = 48 and angle ACB = 60°, AC is calculated as AB / sin(60°) = 48 / (√(3)/2) = 32*√(3). Given that ACDE is a square, its perimeter is AC * 4 = 32*√(3) * 4 = 128*√(3). Answer: C"
}
] |
First perform reasoning, then select the answer from the choices in the following format: Answer: xxx.
<image>
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"path": "depth1_en/27/28_text.jpg"
}
|
Answer:
|
English
|
71
|
depth1
|
text_lite
|
multi_choice
|
[
{
"from": "human",
"value": "First perform reasoning, then select the answer from the choices in the following format: Answer: xxx.\n<image>\nABCD is identified as a parallelogram. DCE takes the form of a sector. AB span 30. Can you calculate the area of the entire shape DCE?\nChoices:\nA.75*π\nB.125*√(3)*π\nC.25*√(3)*π\nD.50*√(3)*π"
},
{
"from": "gpt",
"value": "Given that AB measures 30. Because ABCD is a parallelogram, the opposite side, DC, is also 30. The sector's central angle is 30° and the radius DC equals 30. Hence, the area of sector DCE is 30^2 * π * 30°/360° = 75*π. Answer: A"
}
] |
First perform reasoning, then select the answer from the choices in the following format: Answer: xxx.
<image>
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"path": "depth1_en/28/29_text.jpg"
}
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Answer:
|
English
|
72
|
depth1
|
text_lite
|
multi_choice
|
[
{
"from": "human",
"value": "First perform reasoning, then select the answer from the choices in the following format: Answer: xxx.\n<image>\nCDE is an equilateral triangle. EG span 8*√(2). What is the length of GF in shape ECFG?\nChoices:\nA.7\nB.21*√(2)/2\nC.35*√(3)/3\nD.21/2"
},
{
"from": "gpt",
"value": "Given that AB is 7, the rectangle's opposite sides are equal, so CD is also 7. As CDE is an equilateral triangle, EC = CD = 7. As ECFG is a rectangle, the opposite sides are equal. Hence, GF is also 7. Answer: A"
}
] |
First perform reasoning, then select the answer from the choices in the following format: Answer: xxx.
<image>
|
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"path": "depth1_en/29/30_text.jpg"
}
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Answer:
|
English
|
73
|
depth1
|
text_lite
|
multi_choice
|
[
{
"from": "human",
"value": "First perform reasoning, then select the answer from the choices in the following format: Answer: xxx.\n<image>\nABC conforms a sector. CBD is an isosceles triangle, and the sides CB and BD are of equal length. AB equals to 100. Can you tell me the measures of angle BCD and angle CDB in the isosceles triangle CBD?\nChoices:\nA.75\nB.56.25\nC.300\nD.50"
},
{
"from": "gpt",
"value": "AB is 100. With the sector's radius being constant, BC is 100. CBD is an isosceles triangle where vertex angle B is 30°. Hence, angle BCD and angle CDB are (180° - 30°) / 2 = 75°. Answer: A"
}
] |
First perform reasoning, then select the answer from the choices in the following format: Answer: xxx.
<image>
|
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"path": "depth1_en/3/4_text.jpg"
}
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Answer:
|
English
|
74
|
depth1
|
text_lite
|
multi_choice
|
[
{
"from": "human",
"value": "First perform reasoning, then select the answer from the choices in the following format: Answer: xxx.\n<image>\nABCD is a parallelogram. DCEF forms a square. AB = 1. How do you calculate the area of the shape DCEF?\nChoices:\nA.2*√(3)/3\nB.5*√(2)/2\nC.1\nD.1/2"
},
{
"from": "gpt",
"value": "Given that AB measures 1. Because ABCD is a parallelogram, the opposite side, DC, is also 1. DCEF, being a square, has an area of 1 squared, which is 1. Answer: C"
}
] |
First perform reasoning, then select the answer from the choices in the following format: Answer: xxx.
<image>
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"path": "depth1_en/30/31_text.jpg"
}
|
Answer:
|
English
|
75
|
depth1
|
text_lite
|
open_ended
|
[
{
"from": "human",
"value": "First perform reasoning, then provide the answer in the following format: Answer: xxx.\n<image>\nABCD is geometrically a square. ADEF conforms a square. AB measures 63. How much area does the shape ADEF cover?"
},
{
"from": "gpt",
"value": "AB is 63. Because ABCD is a square, all sides are the same length. Hence, AD = AB = 63. The square ADEF has an area of 63^2, which is 3969. Answer: 3969"
}
] |
First perform reasoning, then provide the answer in the following format: Answer: xxx.
<image>
|
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"path": "depth1_en/31/32_text.jpg"
}
|
Answer:
|
English
|
76
|
depth1
|
text_lite
|
open_ended
|
[
{
"from": "human",
"value": "First perform reasoning, then provide the answer in the following format: Answer: xxx.\n<image>\nABC takes the form of a sector. CBDE takes the form of a parallelogram. Angle CBD is 45°, CE is 84. Could you specify the length of ED in shape CBDE?"
},
{
"from": "gpt",
"value": "AB equals 80. Because the sector's radius is fixed, BC equals 80. Since CBDE is a parallelogram, the opposite side, ED, will also measure 80. Answer: 80"
}
] |
First perform reasoning, then provide the answer in the following format: Answer: xxx.
<image>
|
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"path": "depth1_en/32/33_text.jpg"
}
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Answer:
|
English
|
77
|
depth1
|
text_lite
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open_ended
|
[
{
"from": "human",
"value": "First perform reasoning, then provide the answer in the following format: Answer: xxx.\n<image>\nABCD forms a square. Square CBEF encompasses an inscribed circle. AB totals 55. What is the overall area of the inscribed circle?"
},
{
"from": "gpt",
"value": "AB measures 55. As ABCD is a square, all sides are identical. Therefore, CB = AB = 55. The circle inscribed in square CBEF has a diameter of CB = 55, so its area is (55/2)^2 times π, resulting in 3025*π/4. Answer: 3025*π/4"
}
] |
First perform reasoning, then provide the answer in the following format: Answer: xxx.
<image>
|
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"path": "depth1_en/33/34_text.jpg"
}
|
Answer:
|
English
|
78
|
depth1
|
text_lite
|
open_ended
|
[
{
"from": "human",
"value": "First perform reasoning, then provide the answer in the following format: Answer: xxx.\n<image>\nSquare CBDE encompasses an inscribed circle. Angle ACB measures 45°. In the shape CBDE, what is the measurement of ED?"
},
{
"from": "gpt",
"value": "Given that AB = 60 and angle ACB = 45°, we have BC = AB / tan(45°), which equals 60 / 1 = 60. Since CBDE is a square and all four sides are equal, ED is also CB = 60. Answer: 60"
}
] |
First perform reasoning, then provide the answer in the following format: Answer: xxx.
<image>
|
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"path": "depth1_en/34/35_text.jpg"
}
|
Answer:
|
English
|
79
|
depth1
|
text_lite
|
open_ended
|
[
{
"from": "human",
"value": "First perform reasoning, then provide the answer in the following format: Answer: xxx.\n<image>\nSide CD being an equilateral triangle. Side FG develops into a semi-circle. AB measures 96. Please provide the length of FG in shape DEFG."
},
{
"from": "gpt",
"value": "Knowing that AB is 96, the rectangle's opposite edges are equal, so CD is also 96. Since CDE is an equilateral triangle, DE = CD = 96. FG being the opposite side of DE, is also 96. Thus, the semicircle spanning from F to G and having FG as its diameter, has a length of 96 * π/2 = 48*π. Answer: 48*π"
}
] |
First perform reasoning, then provide the answer in the following format: Answer: xxx.
<image>
|
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"path": "depth1_en/35/36_text.jpg"
}
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Answer:
|
English
|
80
|
depth1
|
text_lite
|
open_ended
|
[
{
"from": "human",
"value": "First perform reasoning, then provide the answer in the following format: Answer: xxx.\n<image>\nSide EF is extended into an equilateral triangle shape inside the rectangle. AB equals to 6. How can we calculate the perimeter of DCEGF?"
},
{
"from": "gpt",
"value": "Given that AB measures 6. Since ABCD is a rectangle, its opposite sides are equal. Thus, DC is also 6. The rectangle DCEF has EF as the opposite side of DC, meaning EF = 6. Since the triangle EFG is equilateral, EG = GF = 6. Therefore, the perimeter is DC + DF + CE + GF + EG = 6 + 12 + 12 + 6 + 6 = 42. Answer: 42"
}
] |
First perform reasoning, then provide the answer in the following format: Answer: xxx.
<image>
|
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"path": "depth1_en/36/37_text.jpg"
}
|
Answer:
|
English
|
81
|
depth1
|
text_lite
|
open_ended
|
[
{
"from": "human",
"value": "First perform reasoning, then provide the answer in the following format: Answer: xxx.\n<image>\nAngle ACB = 45°, CE is 36. What is the total area of shape CBDE?"
},
{
"from": "gpt",
"value": "As AB = 65 and angle ACB = 45°, BC is calculated as AB / tan(45°) = 65 / 1 = 65. The area of CBDE is CB multiplied by CE, which equals 65 multiplied by 36 = 2340. Answer: 2340"
}
] |
First perform reasoning, then provide the answer in the following format: Answer: xxx.
<image>
|
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"path": "depth1_en/37/38_text.jpg"
}
|
Answer:
|
English
|
82
|
depth1
|
text_lite
|
open_ended
|
[
{
"from": "human",
"value": "First perform reasoning, then provide the answer in the following format: Answer: xxx.\n<image>\nDCEF is geometrically a square. AB amounts to 2. What is the perimeter of DCEF?"
},
{
"from": "gpt",
"value": "Given that AB measures 2. Because ABCD is a rectangle, opposite sides must be equal. Hence, DC is also 2. As DCEF is a square, its perimeter is DC * 4 = 2 times 4, giving 8. Answer: 8"
}
] |
First perform reasoning, then provide the answer in the following format: Answer: xxx.
<image>
|
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"path": "depth1_en/38/39_text.jpg"
}
|
Answer:
|
English
|
83
|
depth1
|
text_lite
|
open_ended
|
[
{
"from": "human",
"value": "First perform reasoning, then provide the answer in the following format: Answer: xxx.\n<image>\nABCD conforms a square. Square DCEF has a circle inscribed. AB amounts to 2. What is the measurement of EC in the shape DCEF?"
},
{
"from": "gpt",
"value": "AB is 2. Because ABCD is a square, all sides are the same length. Hence, DC = AB = 2. Since DCEF is a square, all four sides are equal. Therefore, EC = DC = 2. Answer: 2"
}
] |
First perform reasoning, then provide the answer in the following format: Answer: xxx.
<image>
|
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"path": "depth1_en/39/40_text.jpg"
}
|
Answer:
|
English
|
84
|
depth1
|
text_lite
|
open_ended
|
[
{
"from": "human",
"value": "First perform reasoning, then provide the answer in the following format: Answer: xxx.\n<image>\nCBD is identified as a sector. AB = 1, Angle DBC is 90°. Can you tell me the length of arc CD in sector CBD?"
},
{
"from": "gpt",
"value": "With AB = 1 and an angle of 30° at C, BC is AB / tan(30°), which equals 1 / (√(3)/3) = √(3). The sector's central angle is 90° = π/2, and the radius CB is √(3). Thus, the arc length CD equals √(3) * π/2 = √(3)*π/2. Answer: √(3)*π/2"
}
] |
First perform reasoning, then provide the answer in the following format: Answer: xxx.
<image>
|
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"path": "depth1_en/4/5_text.jpg"
}
|
Answer:
|
English
|
85
|
depth1
|
text_lite
|
open_ended
|
[
{
"from": "human",
"value": "First perform reasoning, then provide the answer in the following format: Answer: xxx.\n<image>\nABC is geometrically a sector. CBDE takes the form of a parallelogram. AB equals to 72. What is the full area of the shape CBDE?"
},
{
"from": "gpt",
"value": "AB measures 72. As the radius of the sector is unchanged, BC measures 72. For parallelogram CBDE, which has an angle CBD of 45°, the area is CB * DB * sin(45°) = 72 * 61 * √(2)/2 = 2196*√(2). Answer: 2196*√(2)"
}
] |
First perform reasoning, then provide the answer in the following format: Answer: xxx.
<image>
|
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"path": "depth1_en/40/41_text.jpg"
}
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Answer:
|
English
|
86
|
depth1
|
text_lite
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open_ended
|
[
{
"from": "human",
"value": "First perform reasoning, then provide the answer in the following format: Answer: xxx.\n<image>\nCBD is defined as a sector. Angle DBC amounts to 120°, AB = 98. What is the arc length CD in the sector CBD?"
},
{
"from": "gpt",
"value": "With AB = 98 and an angle of 30° at C, BC is AB / tan(30°), which equals 98 / (√(3)/3) = 98*√(3). The central angle of the sector measures 120° which equals 2*π/3, with the radius CB being 98*√(3). Hence, the arc length CD is 98*√(3) * 2*π/3 = 196*√(3)*π/3. Answer: 196*√(3)*π/3"
}
] |
First perform reasoning, then provide the answer in the following format: Answer: xxx.
<image>
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"path": "depth1_en/41/42_text.jpg"
}
|
Answer:
|
English
|
87
|
depth1
|
text_lite
|
open_ended
|
[
{
"from": "human",
"value": "First perform reasoning, then provide the answer in the following format: Answer: xxx.\n<image>\nSide EF is shaped into an equilateral triangle. AB is equal to 11. In shape DCEGF, what is the length of GE?"
},
{
"from": "gpt",
"value": "Given that AB measures 11. Because ABCD is a rectangle, opposite sides must be equal. Hence, DC is also 11. The rectangle has equal opposite sides, making EF also 11. As EFG forms an equilateral triangle, GE = EF = 11. Answer: 11"
}
] |
First perform reasoning, then provide the answer in the following format: Answer: xxx.
<image>
|
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"path": "depth1_en/42/43_text.jpg"
}
|
Answer:
|
English
|
88
|
depth1
|
text_lite
|
open_ended
|
[
{
"from": "human",
"value": "First perform reasoning, then provide the answer in the following format: Answer: xxx.\n<image>\nABC is an isosceles triangle with AB having the same length as BC. AB totals 1. What is the measurement of the total area of CBD?"
},
{
"from": "gpt",
"value": "With AB being 1, ABC is an isosceles triangle, so BC is also 1. CBD is a right triangle. To find the area, multiply CB by BD and divide by 2, resulting in 1/2. Answer: 1/2"
}
] |
First perform reasoning, then provide the answer in the following format: Answer: xxx.
<image>
|
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"path": "depth1_en/43/44_text.jpg"
}
|
Answer:
|
English
|
89
|
depth1
|
text_lite
|
open_ended
|
[
{
"from": "human",
"value": "First perform reasoning, then provide the answer in the following format: Answer: xxx.\n<image>\nABCD is geometrically a parallelogram. EFG is in the shape of an equilateral triangle. DF is 17. What is the measurement of the perimeter of DCEGF?"
},
{
"from": "gpt",
"value": "Since AB is 9, and ABCD is a parallelogram with equal opposite sides, DC is also 9. The shape DCEF is a rectangle. Because EF is the opposite side of DC, EF = 9. The triangle EFG is equilateral, so EG = GF = 9. Thus, the perimeter is DC + DF + CE + GF + EG = 9 + 17 + 17 + 9 + 9 = 61. Answer: 61"
}
] |
First perform reasoning, then provide the answer in the following format: Answer: xxx.
<image>
|
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"path": "depth1_en/44/45_text.jpg"
}
|
Answer:
|
English
|
90
|
depth1
|
text_lite
|
open_ended
|
[
{
"from": "human",
"value": "First perform reasoning, then provide the answer in the following format: Answer: xxx.\n<image>\nABCD forms a square. DCE conforms a sector. AB = 28. Can you tell me the area of the whole shape DCE?"
},
{
"from": "gpt",
"value": "AB = 28. Since ABCD is a square, all four sides are equal. Therefore, DC = AB = 28. The central angle of the sector is 45°, with a radius of DC equal to 28. Thus, the area of sector DCE is 28^2 * π * 45°/360° = 98*π. Answer: 98*π"
}
] |
First perform reasoning, then provide the answer in the following format: Answer: xxx.
<image>
|
{
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"path": "depth1_en/45/46_text.jpg"
}
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Answer:
|
English
|
91
|
depth1
|
text_lite
|
open_ended
|
[
{
"from": "human",
"value": "First perform reasoning, then provide the answer in the following format: Answer: xxx.\n<image>\nABC is in the form of a sector. CBD takes on a sector shape. Angle DBC totals 45°. What is the overall perimeter of CBD?"
},
{
"from": "gpt",
"value": "AB is 9. Because the radius of the sector remains constant, BC is also 9. The central angle of the sector measures 45° which equals π/4, with the radius CB being 9. Therefore, the arc length CD equals 9 * π/4 = 9*π/4. Hence, the perimeter is 9*2 + 9*π/4 = 9*π/4 + 18. Answer: 9*π/4 + 18"
}
] |
First perform reasoning, then provide the answer in the following format: Answer: xxx.
<image>
|
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"path": "depth1_en/46/47_text.jpg"
}
|
Answer:
|
English
|
92
|
depth1
|
text_lite
|
open_ended
|
[
{
"from": "human",
"value": "First perform reasoning, then provide the answer in the following format: Answer: xxx.\n<image>\nDEF shapes into an equilateral triangle. AE totals 73, AB totals 40. What is the perimeter of ACDFE?"
},
{
"from": "gpt",
"value": "Because AB = 40 and angle ACB is 60°, the length of AC is found by AB / sin(60°) = 40 / (√(3)/2) = 80*√(3)/3. ACDE is a rectangle. Since DE is the opposite side of AC, DE equals 80*√(3)/3. DEF forms an equilateral triangle, making DF equal to FE = 80*√(3)/3. Therefore, the perimeter is AC + AE + CD + FE + DF = 80*√(3)/3 + 73 + 73 + 80*√(3)/3 + 80*√(3)/3 = 80*√(3) + 146. Answer: 80*√(3) + 146"
}
] |
First perform reasoning, then provide the answer in the following format: Answer: xxx.
<image>
|
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"path": "depth1_en/47/48_text.jpg"
}
|
Answer:
|
English
|
93
|
depth1
|
text_lite
|
open_ended
|
[
{
"from": "human",
"value": "First perform reasoning, then provide the answer in the following format: Answer: xxx.\n<image>\nABCD conforms a parallelogram. DCEF conforms a square. AB equals to 1. What is the overall area of the shape DCEF?"
},
{
"from": "gpt",
"value": "Since ABCD is a parallelogram and AB is 1, the opposite side, DC, will also measure 1. Square DCEF has an area calculated as 1 squared, giving 1. Answer: 1"
}
] |
First perform reasoning, then provide the answer in the following format: Answer: xxx.
<image>
|
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"path": "depth1_en/48/49_text.jpg"
}
|
Answer:
|
English
|
94
|
depth1
|
text_lite
|
open_ended
|
[
{
"from": "human",
"value": "First perform reasoning, then provide the answer in the following format: Answer: xxx.\n<image>\nABC is an isosceles triangle where the sides AB and BC are identical in length. CBD is an isosceles triangle, with CB equalling BD. AB amounts to 77. What is the total boundary length of CBD?"
},
{
"from": "gpt",
"value": "With AB being 77, ABC is an isosceles triangle, so BC is also 77. Given that CBD is an isosceles triangle with a vertex angle of 30°, half of its base length equals CB * sin(30°/2) = 77 * (-√(2)/4 + √(6)/4) = 77*√(2 - √(3))/2, making the base length 2 * (77*√(2 - √(3))/2) = 77*√(2 - √(3)). Therefore, the perimeter is CB * 2 + CD = 77 * 2 + 77*√(2 - √(3)) = 77*√(2 - √(3)) + 154. Answer: 77*√(2 - √(3)) + 154"
}
] |
First perform reasoning, then provide the answer in the following format: Answer: xxx.
<image>
|
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"path": "depth1_en/49/50_text.jpg"
}
|
Answer:
|
English
|
95
|
depth1
|
text_lite
|
open_ended
|
[
{
"from": "human",
"value": "First perform reasoning, then provide the answer in the following format: Answer: xxx.\n<image>\nABCD forms a square. CBEF is a parallelogram. Angle CBE amounts to 30°, EB measures 1. In shape CBEF, how long is FE?"
},
{
"from": "gpt",
"value": "AB has the length 1. Given that ABCD is a square and all sides are equal, CB = AB = 1. Given that CBEF is a parallelogram, it means FE will also be 1. Answer: 1"
}
] |
First perform reasoning, then provide the answer in the following format: Answer: xxx.
<image>
|
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"path": "depth1_en/5/6_text.jpg"
}
|
Answer:
|
English
|
96
|
depth1
|
text_lite
|
open_ended
|
[
{
"from": "human",
"value": "First perform reasoning, then provide the answer in the following format: Answer: xxx.\n<image>\nABCD conforms a parallelogram. DCEF is a square. AB equals to 13. What is the overall area of the shape DCEF?"
},
{
"from": "gpt",
"value": "As AB is 13, and ABCD is a parallelogram with equal opposite sides, DC will also be 13. Square DCEF has an area calculated as 13 squared, giving 169. Answer: 169"
}
] |
First perform reasoning, then provide the answer in the following format: Answer: xxx.
<image>
|
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"path": "depth1_en/50/51_text.jpg"
}
|
Answer:
|
English
|
97
|
depth1
|
text_lite
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open_ended
|
[
{
"from": "human",
"value": "First perform reasoning, then provide the answer in the following format: Answer: xxx.\n<image>\nSquare CBDE has a circle inscribed within it. Angle ACB span 45°. What is the total surface area of the circle?"
},
{
"from": "gpt",
"value": "With AB = 10 and angle ACB being 45°, we find BC = AB / tan(45°) = 10 / 1 = 10. The circle inscribed in square CBDE has a radius of CB/2 = 5, giving an area of 5^2 * π = 25*π. Answer: 25*π"
}
] |
First perform reasoning, then provide the answer in the following format: Answer: xxx.
<image>
|
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"path": "depth1_en/51/52_text.jpg"
}
|
Answer:
|
English
|
98
|
depth1
|
text_lite
|
open_ended
|
[
{
"from": "human",
"value": "First perform reasoning, then provide the answer in the following format: Answer: xxx.\n<image>\nACD is in the form of a sector. AB measures 84, Angle ACB equals to 60°. In sector ACD, how long is arc AD?"
},
{
"from": "gpt",
"value": "Given AB = 84 and the angle ACB = 60°, the length of AC is AB / sin(60°), which equals 84 / (√(3)/2) = 56*√(3). The sector's central angle measures 90° which equals π/2, with the radius AC being 56*√(3). Hence, the arc length AD is 56*√(3) * π/2 = 28*√(3)*π. Answer: 28*√(3)*π"
}
] |
First perform reasoning, then provide the answer in the following format: Answer: xxx.
<image>
|
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"path": "depth1_en/52/53_text.jpg"
}
|
Answer:
|
English
|
99
|
depth1
|
text_lite
|
open_ended
|
[
{
"from": "human",
"value": "First perform reasoning, then provide the answer in the following format: Answer: xxx.\n<image>\nABC is an isosceles triangle where AB is the same length as BC. CBD is a sector. Angle DBC totals 90°. What is the length of DB in shape CBD?"
},
{
"from": "gpt",
"value": "Given that AB is 12, ABC being an isosceles triangle means that BC is also 12. Since the radius of the sector is constant, BD = 12. Answer: 12"
}
] |
First perform reasoning, then provide the answer in the following format: Answer: xxx.
<image>
|
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"path": "depth1_en/53/54_text.jpg"
}
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Answer:
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