data_source stringclasses 1
value | images images listlengths 1 1 | prompt listlengths 1 1 | ability stringclasses 1
value | reward_model dict | extra_info dict |
|---|---|---|---|---|---|
multimodal_opensource_math | [
{
"content": "<image>In the diagram, the line JM is perpendicular to the line PH at point E, and the line JM is perpendicular to the line XS at point V. What are the measures of angle JEM and angle JVM?\nLet's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | MATH | {
"ground_truth": "90 degrees f, both angles",
"style": "rule"
} | {
"difficulty": "1",
"index": "e8e8d51a-4321-4695-a713-a2dcaddd396b"
} | |
multimodal_opensource_math | [
{
"content": "<image>In the provided diagram, let's denote angle 1 + angle 2 as variable u (u = 180.0 degrees) and angle 3 as variable v (v = 55.0 degrees). What is the degree measure of angle 4, expressed as variable w in relation to u and v?\nLet's think step by step and output the final answer within \\boxed... | MATH | {
"ground_truth": "55°",
"style": "rule"
} | {
"difficulty": "1",
"index": "99993a6b-5ae3-4388-a218-d0ed4fecc926"
} | |
multimodal_opensource_math | [
{
"content": "<image>In the diagram, there is a circle V. There are lines VJ, VX, VZ in the diagram. Point J, Point X, and Point Z lie on the circle V. Which lines are equal in length to line VJ?\nLet's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | MATH | {
"ground_truth": "VX, VZ",
"style": "rule"
} | {
"difficulty": "1",
"index": "1b556dd0-84fb-40c4-bffa-7d5592800847"
} | |
multimodal_opensource_math | [
{
"content": "<image>In the depicted scenario, Xiaohui's house is situated at point O, and a water tower is positioned at point A, which measures 600.0 units at an angle of 60.0 to the east of her house. What is the distance 'd' from Xiaohui's location to the road in front of her house?\nLet's think step by ste... | MATH | {
"ground_truth": "300",
"style": "rule"
} | {
"difficulty": "1",
"index": "5328ad48-d558-4334-b49d-07f69230320c"
} | |
multimodal_opensource_math | [
{
"content": "<image>A ruler and a right angle triangle board (including a right angle triangle board with a 30° angle) are placed as shown in the figure. If angle 1 = 15°, then the degree of angle 2 is ()\nLet's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | MATH | {
"ground_truth": "45°",
"style": "rule"
} | {
"difficulty": "1",
"index": "db9044e0-71fc-4f75-9fb6-7803f46b4157"
} | |
multimodal_opensource_math | [
{
"content": "<image>In the inscribed quadrilateral ABCD of the circle O, where BC is equal to DC and angle BOC is 130.0, what is the measure of angle BAD? Let the measure of angle BAD be represented as 'θ'\nLet's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | MATH | {
"ground_truth": "130°",
"style": "rule"
} | {
"difficulty": "1",
"index": "09221210-fb10-4854-be71-78a4329e3a08"
} | |
multimodal_opensource_math | [
{
"content": "<image>Point T lies on line DH. Point S lies on line LD. Is line TS perpendicular to line LD?\nLet's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | MATH | {
"ground_truth": "unknown",
"style": "rule"
} | {
"difficulty": "1",
"index": "467712f6-d6fc-4de6-acd2-153b9f8a2514"
} | |
multimodal_opensource_math | [
{
"content": "<image>In the diagram, there is a circle H with a radius of 1.0. What is the area of the circle H?\nLet's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | MATH | {
"ground_truth": "\\pi",
"style": "rule"
} | {
"difficulty": "1",
"index": "b1513730-122f-42c4-99fd-38e4703c4d78"
} | |
multimodal_opensource_math | [
{
"content": "<image>Add 1 shiny blocks. How many objects exist?\nLet's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | MATH | {
"ground_truth": "8",
"style": "rule"
} | {
"difficulty": "1",
"index": "3e7df5c3-12ce-4b8b-bf6f-775c8557d2b3"
} | |
multimodal_opensource_math | [
{
"content": "<image>The height of the street lamp AB in the provided figure is 8.0 units. At a horizontal distance of 4.0 units from the street lamp, there lies a tree labeled CD. If the shadow of the tree under the light DE measures 3.0 units, what is the height of the tree?\nLet's think step by step and outp... | MATH | {
"ground_truth": "\\frac{24}{7}米",
"style": "rule"
} | {
"difficulty": "1",
"index": "5151f44a-9f0e-4eb2-9711-2d7f77320cb7"
} | |
multimodal_opensource_math | [
{
"content": "<image>How many objects are left if you subtract all cylinders and then subtract all spheres?\nLet's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | MATH | {
"ground_truth": "1",
"style": "rule"
} | {
"difficulty": "1",
"index": "44e71f33-9dfe-4a9e-aeea-591660294bfc"
} | |
multimodal_opensource_math | [
{
"content": "<image>There is a square in the diagram, represented by the symbol VNRL. Which lines are equal in length to line VN?\nLet's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | MATH | {
"ground_truth": "NR, RL, LV",
"style": "rule"
} | {
"difficulty": "1",
"index": "f97db367-57a7-4830-a909-962e194d09cf"
} | |
multimodal_opensource_math | [
{
"content": "<image>How many green objects are there?\nLet's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | MATH | {
"ground_truth": "2",
"style": "rule"
} | {
"difficulty": "1",
"index": "9e8bd7ee-df75-4497-a6fb-035b7a9e89b8"
} | |
multimodal_opensource_math | [
{
"content": "<image>As shown in the figure, there is chord AB in circle O with radius 4.0, which is folded in half with AB as the crease, and the inferior arc just passes through the center O, then the length of chord AB is equal to ()\nLet's think step by step and output the final answer within \\boxed{}.",
... | MATH | {
"ground_truth": "4√{3}",
"style": "rule"
} | {
"difficulty": "1",
"index": "e1ec9695-b572-44d1-9d5a-9d8a93df8e9f"
} | |
multimodal_opensource_math | [
{
"content": "<image>What is the perimeter of the trapezoid?\nLet's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | MATH | {
"ground_truth": "11 + x + 13 + 14 + 14",
"style": "rule"
} | {
"difficulty": "1",
"index": "a21f2511-8ea4-47e6-9866-5b435abb1f80"
} | |
multimodal_opensource_math | [
{
"content": "<image>Given that \\( E C \\) and \\( A B \\) are diameters of \\(\\odot O\\), and \\(\\angle EOF = 45^\\circ\\), find the measure of \\(\\angle AOF\\)\nLet's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | MATH | {
"ground_truth": "135 degrees",
"style": "rule"
} | {
"difficulty": "1",
"index": "9ce7319f-da03-494f-a84d-18098fde3bb3"
} | |
multimodal_opensource_math | [
{
"content": "<image>Find the value of \\( y \\) given that \\( x = 16 \\) in the figure\nLet's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | MATH | {
"ground_truth": "40",
"style": "rule"
} | {
"difficulty": "1",
"index": "11f30dd0-5928-4be7-a87e-af4c4837c3f4"
} | |
multimodal_opensource_math | [
{
"content": "<image>If the side length of the larger square ABCD is 12 and BF is 3, what is the length of segment AH?\nLet's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | MATH | {
"ground_truth": "√135 / 2",
"style": "rule"
} | {
"difficulty": "1",
"index": "1bd1a2bc-8ed0-4dd0-ada7-73f9f5b91854"
} | |
multimodal_opensource_math | [
{
"content": "<image>如图,在⊙O中,圆心角∠BOC=80°,则圆周角∠BAC的度数为()\nLet's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | MATH | {
"ground_truth": "40°",
"style": "rule"
} | {
"difficulty": "1",
"index": "3844cfcc-535e-4fbb-8ac7-9290e065f3b5"
} | |
multimodal_opensource_math | [
{
"content": "<image>A large parasol can be approximately regarded as a conical shape when the surface of umbrella is stretched. As shown in the figure, the length of its generatrix is 2.5 and its height is 1.5, so the area of fabric used to make this parasol (not counting the seams) is ()\nLet's think step b... | MATH | {
"ground_truth": "5πm^{2}",
"style": "rule"
} | {
"difficulty": "1",
"index": "59817ac5-66e1-400e-9dd2-5e44fbc6fea5"
} | |
multimodal_opensource_math | [
{
"content": "<image>If the area of the ABC sector is 157, the length of the BD side is 6 and the diagonal of the BDEC rectangle is 14, compute the degree of the CBA angle. Assume $\\pi=3.14$. Round computations to 2 decimal places.\nLet's think step by step and output the final answer within \\boxed{}.",
"... | MATH | {
"ground_truth": "111.6",
"style": "rule"
} | {
"difficulty": "1",
"index": "b453563d-1634-4c78-9a0e-14f02e689ea5"
} | |
multimodal_opensource_math | [
{
"content": "<image>In a scenario where a tree broke and fell, the distance from the top of the tree to the ground is represented as 'x' units, and the distance from the top to the trunk is denoted as 'y' units. Determine the original height of the tree before it broke\nLet's think step by step and output the ... | MATH | {
"ground_truth": "8米",
"style": "rule"
} | {
"difficulty": "1",
"index": "39845af3-75b7-4f9f-ba4b-8b9ef8c53210"
} | |
multimodal_opensource_math | [
{
"content": "<image>In the given quadrilateral ABCD, where AB is parallel to CD and AD is parallel to BC, the angular bisectors AE and DF of angle BAD and angle ADC intersect BC at points E and F respectively. If EF = 2.0 and AB = 5.0, what is the length of AD?\nLet's think step by step and output the final an... | MATH | {
"ground_truth": "8",
"style": "rule"
} | {
"difficulty": "1",
"index": "b1fbc08f-5cf3-4906-adf2-286473678f9d"
} | |
multimodal_opensource_math | [
{
"content": "<image>Line HB is the line connecting the midpoint H of line DG and the midpoint B of line GW. What is the length of HB if the length of WR is 1?\nLet's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | MATH | {
"ground_truth": "0.5",
"style": "rule"
} | {
"difficulty": "1",
"index": "ef3e07de-20d8-40bf-9d56-e3a4cf361607"
} | |
multimodal_opensource_math | [
{
"content": "<image>In the provided diagram, let's represent the radius of the sector-shaped AOB as variable 'r' (r = 3.0) and the degree of the central angle as variable 'x' (x = 120.0). What is the equation for the lateral area of the enclosed cone in terms of 'r' and 'x'?\nLet's think step by step and outpu... | MATH | {
"ground_truth": "3πcm^{2}",
"style": "rule"
} | {
"difficulty": "1",
"index": "ee5be098-1bdc-47d7-a198-ec35e3bbd94a"
} | |
multimodal_opensource_math | [
{
"content": "<image>In the given parallelogram ABCD, where diagonal AC intersects diagonal BD at point O and AB is perpendicular to AC, let's denote the length of CD as variable x (x = 8) and the length of AC as variable y (y = 12). What is the length of DB, expressed as variable z in terms of x and y?\nLet's ... | MATH | {
"ground_truth": "20",
"style": "rule"
} | {
"difficulty": "1",
"index": "0476a101-ce79-4f6e-a6c2-31f6cb974883"
} | |
multimodal_opensource_math | [
{
"content": "<image>What is the length of line ET?\nLet's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | MATH | {
"ground_truth": "The length of line ET is 5",
"style": "rule"
} | {
"difficulty": "1",
"index": "82081988-d54d-4e0f-9254-5afcb2222d35"
} | |
multimodal_opensource_math | [
{
"content": "<image>Consider the inscribed quadrilateral ABCD in circle O, where the measure of angle BOD is 'a'. Calculate the measure of angle DCB in relation to 'a'\nLet's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | MATH | {
"ground_truth": "50°",
"style": "rule"
} | {
"difficulty": "1",
"index": "14065ee4-00a9-4bce-96ce-d2241555f48e"
} | |
multimodal_opensource_math | [
{
"content": "<image>In triangle ABC, if D and E are the midpoints of sides AB and AC respectively, G is the midpoint of EC, and DG extended intersects the extended line of BC at point F, and the area of triangle GCF is 2, what is the area of triangle ABC?\nLet's think step by step and output the final answer w... | MATH | {
"ground_truth": "16",
"style": "rule"
} | {
"difficulty": "1",
"index": "dd9bcb3a-1721-4a2c-ba5e-9cb9f4f4b364"
} | |
multimodal_opensource_math | [
{
"content": "<image>Refer to the figure at the right. Find the perimeter of the triangle\nLet's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | MATH | {
"ground_truth": "28.39",
"style": "rule"
} | {
"difficulty": "1",
"index": "412e1ec6-d1dd-4242-b433-6ce3ac547b6e"
} | |
multimodal_opensource_math | [
{
"content": "<image>If AC and BD intersect at point O in rectangle ABCD, and the midpoints of AB and OA are represented by M and N, respectively, what is the length of AC if MN measures 2 units?\nLet's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | MATH | {
"ground_truth": "8",
"style": "rule"
} | {
"difficulty": "1",
"index": "45d69623-60d3-485a-893a-8c6dc46e694a"
} | |
multimodal_opensource_math | [
{
"content": "<image>There is a hexagon in the diagram, represented by the symbol MYHSOV. What is the length of line OV?\nLet's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | MATH | {
"ground_truth": "2",
"style": "rule"
} | {
"difficulty": "1",
"index": "4badff2f-101e-4547-b358-5d7f9092dbcb"
} | |
multimodal_opensource_math | [
{
"content": "<image>In the provided rectangle ABCD, where diagonal AC intersects diagonal BD at point O and E is the midpoint of BC, let's denote the length of AC as variable 'u' (u = 8) and the degree measure of angle ACB as variable 'v' (v = 30°). What is the value of OE, denoted as variable 'w', in terms of... | MATH | {
"ground_truth": "2",
"style": "rule"
} | {
"difficulty": "1",
"index": "b709b88c-40de-4f93-b9db-efd3dd798cc8"
} | |
multimodal_opensource_math | [
{
"content": "<image>If the ABCD shape is a rectangle where a semi-circle has been removed from one side of it, the perimeter of the ABCD shape is 102, the BCFGH shape is a combination of a rectangle and an equilateral triangle, the perimeter of the BCFGH shape is 90, the length of the CF side is $x + 8.31$ and... | MATH | {
"ground_truth": "24.61",
"style": "rule"
} | {
"difficulty": "1",
"index": "fcdd88d1-47f4-4432-b5df-22da807df7b7"
} | |
multimodal_opensource_math | [
{
"content": "<image>Place a set square (angle A = 45°, angle E = 60°) as shown in the figure. Point F is on the extension line of CB. If DE parallel CF, then angle BDF = ()\nLet's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | MATH | {
"ground_truth": "15°",
"style": "rule"
} | {
"difficulty": "1",
"index": "48c2e35d-ec3c-4f55-8884-5e8d978cd67b"
} | |
multimodal_opensource_math | [
{
"content": "<image>If the blue shape is a combination of a rectangle and a semi-circle, the perimeter of the blue shape is 96, the length of the height perpendicular to the base marked with \"$b$\" in the lime triangle is 6, the length of the height perpendicular to the base marked with \"$a$\" in the lime tr... | MATH | {
"ground_truth": "22.3",
"style": "rule"
} | {
"difficulty": "1",
"index": "bdbf8e64-2d97-4eca-ac61-0f1e7933190b"
} | |
multimodal_opensource_math | [
{
"content": "<image>In the provided figure, with the height of the highway bridge from the ground AC measuring 6.0 and the horizontal width BC of the approach bridge AB measuring 24.0, it is decided to change the slope of the approach bridge to AD to be 1.0:6.0. What is the length of BD in this scenario?\nLet'... | MATH | {
"ground_truth": "12米",
"style": "rule"
} | {
"difficulty": "1",
"index": "a8d0e1d8-cb2c-44d4-aeb1-d2640ceb0f1f"
} | |
multimodal_opensource_math | [
{
"content": "<image>Compute the degree of the angle marked with question mark. Round computations to 2 decimal places.\nLet's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | MATH | {
"ground_truth": "66.93",
"style": "rule"
} | {
"difficulty": "1",
"index": "8af692c8-3814-486a-8309-ba9a9e5e3e27"
} | |
multimodal_opensource_math | [
{
"content": "<image>In the given figure, points A, B, and D are vertices of parallelogram ABCD, where these points lie on circle O. Moreover, point C lies on the diameter BE of circle O. If angle ADC measures 54.0 degrees and we connect points A and E, what is the measure of angle AEB?\nLet's think step by ste... | MATH | {
"ground_truth": "36°",
"style": "rule"
} | {
"difficulty": "1",
"index": "89f97dbc-ae1f-4349-9a2a-78e09e61b781"
} | |
multimodal_opensource_math | [
{
"content": "<image>What is the ratio of spheres to cylinders?\nLet's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | MATH | {
"ground_truth": "1:1",
"style": "rule"
} | {
"difficulty": "1",
"index": "3fd07c0a-a04d-47fc-a590-d97a29f0eb7b"
} | |
multimodal_opensource_math | [
{
"content": "<image>If the length of the height perpendicular to the base marked with \"$a$\" in the cyan triangle is 22, the blue shape is a combination of a rectangle and a semi-circle, the perimeter of the blue shape is 100 and the perimeter of the brown rectangle is 66, compute the area of the cyan triangl... | MATH | {
"ground_truth": "253.22",
"style": "rule"
} | {
"difficulty": "1",
"index": "0e3a0ed8-4208-429e-bc64-ba365f12a2fc"
} | |
multimodal_opensource_math | [
{
"content": "<image>In the diagram, there is a circle F with a radius of 0.6. The line OQ passes through the center of the circle at point F and is the diameter. What is the length of the line OQ?\nLet's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | MATH | {
"ground_truth": "1.2",
"style": "rule"
} | {
"difficulty": "1",
"index": "5e8df919-d297-43a9-b159-66aba76f34e5"
} | |
multimodal_opensource_math | [
{
"content": "<image>In the given figure, a rhombus ABCD is depicted with diagonal intersection point O. If angle ABC is measured at 50 degrees and E lies on segment AO, what is the measurement of angle BEC?\nLet's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | MATH | {
"ground_truth": "65°",
"style": "rule"
} | {
"difficulty": "1",
"index": "9bd31aca-579e-4cd5-a0d8-69082abe04d7"
} | |
multimodal_opensource_math | [
{
"content": "<image>In the given figure, the roads AC and BC are perpendicular to each other. The midpoint M of road AB is separated from point C by a lake. If the length of AB is measured to be 2.4km, then what is the distance between points M and C?\nLet's think step by step and output the final answer withi... | MATH | {
"ground_truth": "1.2",
"style": "rule"
} | {
"difficulty": "1",
"index": "aedbe07d-0813-4eca-8f53-9e1954ded814"
} | |
multimodal_opensource_math | [
{
"content": "<image>Given the provided figure where triangle ABC is inscribed within circle O, if OB and OC are connected and angle BOC measures 120.0 degrees, what is the measure of angle BAC?\nLet's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | MATH | {
"ground_truth": "60°",
"style": "rule"
} | {
"difficulty": "1",
"index": "16c47ca4-3f50-4d44-9573-8b979aa1e8b5"
} | |
multimodal_opensource_math | [
{
"content": "<image>如图,点C是⊙O的直径AB延长线上一点,CD切⊙O于点D,DE为⊙O的弦,若∠AED=60°,⊙O的半径是2．求三角形ADE的面积。\nLet's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | MATH | {
"ground_truth": "\\( \\sqrt{3} \\)",
"style": "rule"
} | {
"difficulty": "1",
"index": "4b4e962f-103a-48f6-ae32-1e0111e7f6ca"
} | |
multimodal_opensource_math | [
{
"content": "<image>There is a line QG between point Q and point G. What is the length of line QG if the length of line GW is 10?\nLet's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | MATH | {
"ground_truth": "10",
"style": "rule"
} | {
"difficulty": "1",
"index": "472f5a12-83d5-43ac-8cac-7c801590ccfc"
} | |
multimodal_opensource_math | [
{
"content": "<image>Given that AB is the diameter of circle O and OD is parallel to AC, what is the length of OC if the radius of the circle is 5 units?\nLet's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | MATH | {
"ground_truth": "5 units",
"style": "rule"
} | {
"difficulty": "1",
"index": "08c86435-8939-4c31-a905-b0ffa776fc47"
} | |
multimodal_opensource_math | [
{
"content": "<image>In the diagram, there is a pentagon VFSHE with all angles equal to 108 degrees. Is this possible?\nLet's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | MATH | {
"ground_truth": "yes",
"style": "rule"
} | {
"difficulty": "1",
"index": "5f75a3c8-e146-4ea5-a7e8-4224e7085d32"
} | |
multimodal_opensource_math | [
{
"content": "<image>In the context of right triangle ABC with a right angle at C, where the lengths of sides are specified as 'm' and 'n' (m = 3, n = 4), and point P resides on side AB, consider the perpendiculars PE and PF drawn from point P to sides AC and BC, creating rectangle PECF. What is the minimum len... | MATH | {
"ground_truth": "2.4",
"style": "rule"
} | {
"difficulty": "1",
"index": "d7d3eaf4-f279-439e-8756-7f27bcd0b741"
} | |
multimodal_opensource_math | [
{
"content": "<image>Considering the figure provided, triangle ABC is shown with point M representing the midpoint of edge BC. Line AN serves as the angle bisector for angle BAC, while BN intersects line AN perpendicularly at point N. AB is measured at a length of 8.0, and MN is given as 3.0. Calculate the leng... | MATH | {
"ground_truth": "14",
"style": "rule"
} | {
"difficulty": "1",
"index": "121b1bab-f750-4cff-88e5-4ed0b62f9d79"
} | |
multimodal_opensource_math | [
{
"content": "<image>As depicted in the diagram, triangle ABC has an angle A measuring 50.0 degrees. The inscribed circle I is tangentially intersecting the edges BC, CA, and AB at points D, E, and F respectively. What is the measurement of angle EDF?\nLet's think step by step and output the final answer within... | MATH | {
"ground_truth": "65°",
"style": "rule"
} | {
"difficulty": "1",
"index": "51957630-9917-4027-9235-33d88f4ca7ae"
} | |
multimodal_opensource_math | [
{
"content": "<image>If the area of the cyan parallelogram is 84, compute the degree of the angle marked with question mark. Round computations to 2 decimal places.\nLet's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | MATH | {
"ground_truth": "53.13",
"style": "rule"
} | {
"difficulty": "1",
"index": "512d7343-9965-4eea-863c-90471f90d5b8"
} | |
multimodal_opensource_math | [
{
"content": "<image>In the given diagram, let's denote the degree measure of angle BAC as variable p where p = 54°. What is the degree measure of angle BOC, expressed as variable q in terms of p?\nLet's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | MATH | {
"ground_truth": "108°",
"style": "rule"
} | {
"difficulty": "1",
"index": "5fd14f75-355c-4436-b0eb-00ccc8e8c6ac"
} | |
multimodal_opensource_math | [
{
"content": "<image>Given a parallelogram ABCD where AB = 10.0 and BF = 12.0, construct the bisector of angle BAD intersecting BC at point E. Calculate the length of AE\nLet's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | MATH | {
"ground_truth": "16",
"style": "rule"
} | {
"difficulty": "1",
"index": "16a11698-e9d1-4c10-b75c-7b675500c6cb"
} | |
multimodal_opensource_math | [
{
"content": "<image>There is a triangle PLF. The measure of angle LPF is 70 degrees. What is the sum of the measures of angles PFL and FLP?\nLet's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | MATH | {
"ground_truth": "110 degrees",
"style": "rule"
} | {
"difficulty": "1",
"index": "74654acf-dcab-4d2a-824e-b03b49a56b73"
} | |
multimodal_opensource_math | [
{
"content": "<image>If you subtract 0 purple cylinders, how many objects remain?\nLet's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | MATH | {
"ground_truth": "9",
"style": "rule"
} | {
"difficulty": "1",
"index": "3b9e2a4e-9b32-417d-9491-878882577d8d"
} | |
multimodal_opensource_math | [
{
"content": "<image>A student with a height of 0.8 wants to measure the height of a big tree. She walks along the tree shadow BA from B to A. When reaching point C, the top of her shadow coincides with the top of the tree's shadow. If BC measures 2.0 and CA measures 0.5, what is the height of the tree?\nLet's ... | MATH | {
"ground_truth": "4.0",
"style": "rule"
} | {
"difficulty": "1",
"index": "f0f27f88-96cc-4954-a8dd-9b457f1ff062"
} | |
multimodal_opensource_math | [
{
"content": "<image>In the diagram, the line RA is the tangent line of the circle G at point A, and the line RK is the tangent line of the circle G at point K. The measure of the angle ARK is 74 degrees. What is the measure of angle RAG?\nLet's think step by step and output the final answer within \\boxed{}.",... | MATH | {
"ground_truth": "90 degrees",
"style": "rule"
} | {
"difficulty": "1",
"index": "9e7ad656-871f-4004-ace6-f8806c5e4931"
} | |
multimodal_opensource_math | [
{
"content": "<image>If points A, B, and C all lie on circle O and angle A is measured at 50.0 degrees, what is the degree measure of angle BOC as depicted in the figure?\nLet's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | MATH | {
"ground_truth": "100°",
"style": "rule"
} | {
"difficulty": "1",
"index": "4fe45fec-b54d-4ec6-8822-2644b3047a66"
} | |
multimodal_opensource_math | [
{
"content": "<image>What is the area of the circle with center O and radius OC of 10 cm?\nLet's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | MATH | {
"ground_truth": "100π cm^2",
"style": "rule"
} | {
"difficulty": "1",
"index": "73b6cfcf-aea9-47d2-8870-6a8e056327e7"
} | |
multimodal_opensource_math | [
{
"content": "<image>As shown in the figure, AF divides angle BAC into two equal angles. The line segment EF, which is parallel to AC, intersects AB at point E. Given that angle 1 measures 30°, what is the degree measure of angle BEF?\nLet's think step by step and output the final answer within \\boxed{}.",
... | MATH | {
"ground_truth": "60°",
"style": "rule"
} | {
"difficulty": "1",
"index": "8025cfcf-d1d9-47f5-aea6-e216ed5c75fd"
} | |
multimodal_opensource_math | [
{
"content": "<image>In the diagram, if the measure of angle ABC is 50°, what is the measure of angle AOE?\nLet's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | MATH | {
"ground_truth": "115°",
"style": "rule"
} | {
"difficulty": "1",
"index": "20e3bb56-cf60-4e59-b980-46c1102012eb"
} | |
multimodal_opensource_math | [
{
"content": "<image>In the provided diagram, we are shown right triangle ABC, where angle C is given as 90 degrees. The angle bisector of BAC, AD, intersects side BC at point D. If the area of triangle ACD is 6 square units and the length of side AC measures 6 units, what is the distance between point D and si... | MATH | {
"ground_truth": "2",
"style": "rule"
} | {
"difficulty": "1",
"index": "6686dd1c-a04b-4f9f-b5ba-ac96958ee293"
} | |
multimodal_opensource_math | [
{
"content": "<image>There is a regular hexagon in the diagram, represented by the symbol XKIELU. The length of line EL is 2. What is the length of line XK?\nLet's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | MATH | {
"ground_truth": "2",
"style": "rule"
} | {
"difficulty": "1",
"index": "16f2a7b1-f7ed-4168-ab56-0bb3552e5058"
} | |
multimodal_opensource_math | [
{
"content": "<image>In the diagram featuring circle O and points A, B, and C connected by line segments AB, AC, OB, and OC, along with tangent line BD intersecting the extension of line OC at point D, if angle A measures 25 degrees, what is the degree measure of angle D?\nLet's think step by step and output th... | MATH | {
"ground_truth": "40°",
"style": "rule"
} | {
"difficulty": "1",
"index": "5e7524fb-ed4d-4467-b48e-194643ff4af7"
} | |
multimodal_opensource_math | [
{
"content": "<image>Find the chromatic number of the following graph.\nLet's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | MATH | {
"ground_truth": "2",
"style": "rule"
} | {
"difficulty": "1",
"index": "4050bf4e-d96a-49a7-9f92-cb5d32306714"
} | |
multimodal_opensource_math | [
{
"content": "<image>As shown in the figure, if the diameter of circle O is known as AE = 10.0, angle B = angle EAC, then the length of AC is ()\nLet's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | MATH | {
"ground_truth": "5√{2}cm",
"style": "rule"
} | {
"difficulty": "1",
"index": "cce918fa-96c8-4e56-b294-6d770386f06a"
} | |
multimodal_opensource_math | [
{
"content": "<image>Given the isosceles trapezoid shown in the figure, let's represent the ratio of the slopes of the waist as variable i, where i = 3.0:2.0. If the top width of the subgrade is 7.0 and the subgrade height is 6.0, what is the value of the bottom width of the subgrade, denoted as variable x in r... | MATH | {
"ground_truth": "15米",
"style": "rule"
} | {
"difficulty": "1",
"index": "207d8293-37ad-4811-90a3-6fab120a12ff"
} | |
multimodal_opensource_math | [
{
"content": "<image>Line KA is the line connecting the midpoint K of line WS and the midpoint A of line MR. The length of line MR is 8. What is the length of line AM?\nLet's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | MATH | {
"ground_truth": "4",
"style": "rule"
} | {
"difficulty": "1",
"index": "69d6ae5a-5917-4dc0-9f53-bd00faa426ea"
} | |
multimodal_opensource_math | [
{
"content": "<image>There is a parallelogram in the diagram, represented by the symbol MWYX. Line MP is the line connecting point M and the midpoint P of line YX. If the length of line WY is 8, what is the length of line MX?\nLet's think step by step and output the final answer within \\boxed{}.",
"role": ... | MATH | {
"ground_truth": "8",
"style": "rule"
} | {
"difficulty": "1",
"index": "4b5f2db2-6f15-4ab2-8d8b-434916565eda"
} | |
multimodal_opensource_math | [
{
"content": "<image>In the diagram, the length of line CE is 3.8, and the length of line CV is 1.9. What is the ratio of the radii of the two circles?\nLet's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | MATH | {
"ground_truth": "2:1",
"style": "rule"
} | {
"difficulty": "1",
"index": "16b3db3d-e71c-4600-adec-9408bcb2ad11"
} | |
multimodal_opensource_math | [
{
"content": "<image>In triangle ABC, let the length of AD be represented by variable p (p = 4.0), the length of DB be represented by variable q (q = 6.0), and the length of AE be represented by variable r (r = 3.0). If DE is parallel to BC, what is the value of AC denoted by variable s in relation to p, q, and... | MATH | {
"ground_truth": "7.5",
"style": "rule"
} | {
"difficulty": "1",
"index": "0aabdc1b-b789-43ef-9053-19abd9012652"
} | |
multimodal_opensource_math | [
{
"content": "<image>In the given figure, let's denote the angle BAC as variable x where x = 55.0 degrees. What is the degree measure of the angle BOC, expressed as variable y in relation to x?\nLet's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | MATH | {
"ground_truth": "110°",
"style": "rule"
} | {
"difficulty": "1",
"index": "e8fa9605-d259-4a5f-9c4e-ea058a0fbceb"
} | |
multimodal_opensource_math | [
{
"content": "<image>In the diagram, there is a circle K with a radius of 2.13. What is the area of the circle K? Approximating π≈3.14.\nLet's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | MATH | {
"ground_truth": "14.23",
"style": "rule"
} | {
"difficulty": "1",
"index": "cb005205-9f95-4bf6-836d-bcee1741fccd"
} | |
multimodal_opensource_math | [
{
"content": "<image>Line LV is the line connecting the midpoint L of line TA and the midpoint V of line CJ. What is the length of line LT if the length of line TA is 10?\nLet's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | MATH | {
"ground_truth": "5",
"style": "rule"
} | {
"difficulty": "1",
"index": "f71da3c4-3262-4963-935e-d0cabee073ea"
} | |
multimodal_opensource_math | [
{
"content": "<image>In order to determine the height 'x' of a tree, Xiaogang uses a measuring bamboo pole of length 'L'. Positioning the pole so that its shadow and the top of the tree cast shadows on the ground at the same point, the pole is 6.0 units away from this point and the tree is 15.0 units away. What... | MATH | {
"ground_truth": "5m",
"style": "rule"
} | {
"difficulty": "1",
"index": "48afc6bf-55b0-4554-bb04-d42441504075"
} | |
multimodal_opensource_math | [
{
"content": "<image>In the figure provided, if the measure of angle 1 is 47°, then what is the degree measure of angle 2? Represent the measure of angle 2 as θ\nLet's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | MATH | {
"ground_truth": "137°",
"style": "rule"
} | {
"difficulty": "1",
"index": "2adbc54b-f04a-4f3c-b711-5286c4b26302"
} | |
multimodal_opensource_math | [
{
"content": "<image>In the diagram, triangle ABC has a perimeter of 21 units. Points O, B, and C are such that OB and OC bisect angles ABC and ACB, respectively. Additionally, OD is perpendicular to BC at point D, with OD measuring 4 units. What is the area of triangle ABC? Represent the area as 'A'\nLet's thi... | MATH | {
"ground_truth": "42",
"style": "rule"
} | {
"difficulty": "1",
"index": "76b824fa-df53-4e01-9c95-649fa10e45e2"
} | |
multimodal_opensource_math | [
{
"content": "<image>As shown in the figure, AB is the diameter of O. If the angel of circumference angle CBA = 40.0, then the angel of circumference angle CAB = ()\nLet's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | MATH | {
"ground_truth": "50°",
"style": "rule"
} | {
"difficulty": "1",
"index": "2bb970da-0eca-4eba-b0cc-30a04488f826"
} | |
multimodal_opensource_math | [
{
"content": "<image>As shown in the figure, if the length of the generatrix of the cone is 5cm and the length of the slant height is 4cm, then the area of the base of the cone is ()\nLet's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | MATH | {
"ground_truth": "9πcm2",
"style": "rule"
} | {
"difficulty": "1",
"index": "701cbced-a004-43a9-970a-b767d46011d5"
} | |
multimodal_opensource_math | [
{
"content": "<image>If the length of WZ is 15 units, what is the length of XY?\nLet's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | MATH | {
"ground_truth": "15 units",
"style": "rule"
} | {
"difficulty": "1",
"index": "2b3300b0-dd9c-4d57-a559-6d4172e28fc7"
} | |
multimodal_opensource_math | [
{
"content": "<image>If the area of the cyan rectangle is 114, compute the length of the side of the cyan rectangle marked with question mark. Round computations to 2 decimal places.\nLet's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | MATH | {
"ground_truth": "5.7",
"style": "rule"
} | {
"difficulty": "1",
"index": "aadaabe1-1c9b-40ed-b836-d7ff19e06d19"
} | |
multimodal_opensource_math | [
{
"content": "<image>In the diagram, there is a circle D with a radius DC = 3.1. What is the diameter of the circle D?\nLet's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | MATH | {
"ground_truth": "6.2",
"style": "rule"
} | {
"difficulty": "1",
"index": "cf266e90-7528-48a1-9e45-e527befe5809"
} | |
multimodal_opensource_math | [
{
"content": "<image>What is the measure of angle A in triangle ABC?\nLet's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | MATH | {
"ground_truth": "62 degrees",
"style": "rule"
} | {
"difficulty": "1",
"index": "8a0e9073-bc0b-4040-b28f-80387d381fa5"
} | |
multimodal_opensource_math | [
{
"content": "<image>Q R S T is a rectangle. If Q P = 3 x + 11 and P S = 4 x + 8, find the length of the diagonal.\nLet's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | MATH | {
"ground_truth": "40",
"style": "rule"
} | {
"difficulty": "1",
"index": "322dc84a-6867-49e6-b6a9-34c41a4396e2"
} | |
multimodal_opensource_math | [
{
"content": "<image>如图,在△ABC中,AB=AC,CD∥AB,点E在BC的延长线上.若∠A=30°,则∠DCE的大小为()\nLet's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | MATH | {
"ground_truth": "75°",
"style": "rule"
} | {
"difficulty": "1",
"index": "99087b75-ed55-4bd1-bbac-fc939849e7cc"
} | |
multimodal_opensource_math | [
{
"content": "<image>In the diagram, there is a circle Z with a radius of 1.7. The line MO and YJ are diameters of the circle Z. What is the length of MO and YJ?\nLet's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | MATH | {
"ground_truth": "3.4",
"style": "rule"
} | {
"difficulty": "1",
"index": "641baa4f-845e-40ab-b44c-2cd838205fec"
} | |
multimodal_opensource_math | [
{
"content": "<image>In the provided figure, let angle 1 be represented by the variable a (a = 110.0) and angle 2 be represented by the variable b (b = 40.0). What is the value of angle 3, denoted as variable c, in relation to a and b?\nLet's think step by step and output the final answer within \\boxed{}.",
... | MATH | {
"ground_truth": "70°",
"style": "rule"
} | {
"difficulty": "1",
"index": "3d229efd-d195-4480-8332-8766416a909c"
} | |
multimodal_opensource_math | [
{
"content": "<image>If the ABCD shape is a square where a circle has been removed from it, compute the area of the ABCD shape. Assume $\\pi=3.14$. Round computations to 2 decimal places.\nLet's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | MATH | {
"ground_truth": "36.76",
"style": "rule"
} | {
"difficulty": "1",
"index": "785eccd8-80b8-484a-99a2-6ada58fa0470"
} | |
multimodal_opensource_math | [
{
"content": "<image>In the given diagram, if angle β is 85° and angle 2 is 60°, what is the measure of angle α?\nLet's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | MATH | {
"ground_truth": "145°",
"style": "rule"
} | {
"difficulty": "1",
"index": "d7ff0422-e907-4c1f-a4cf-af7c5fcebd34"
} | |
multimodal_opensource_math | [
{
"content": "<image>In the diagram, there is a circle U. The measure of the angle between the line EZ and the circle U at the point M is equal to 68 degrees. What is the central angle of the arc formed by points E and M on circle U?\nLet's think step by step and output the final answer within \\boxed{}.",
... | MATH | {
"ground_truth": "136 degrees",
"style": "rule"
} | {
"difficulty": "1",
"index": "ed498959-5919-4d0f-bcf3-2413d0dde6b8"
} | |
multimodal_opensource_math | [
{
"content": "<image>As shown in the picture, to measure the distance between points A and B separated by a pond, we can select a point C outside AB, connect AC, BC, and find their respective midpoints D and E. Then connect DE. If we measure AC = 30m, BC = 40m, and DE = 24m, then AB = ()\nLet's think step by st... | MATH | {
"ground_truth": "48m",
"style": "rule"
} | {
"difficulty": "1",
"index": "e4869a20-3915-4133-a657-0bdfc148dbd1"
} | |
multimodal_opensource_math | [
{
"content": "<image>In the scenario presented, a square ABCD is inscribed within a circle O, and point P lies on the side AB. Determine the degree of angle BPC using an unknown variable denoted by 'beta'\nLet's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | MATH | {
"ground_truth": "45°",
"style": "rule"
} | {
"difficulty": "1",
"index": "217d43aa-aac5-40f1-b555-6be0bbd5fd9a"
} | |
multimodal_opensource_math | [
{
"content": "<image>What is the length of the slope AC of the overpass if the height AB is 6.0 and the angle between the slope AC and the ground BC is represented by angle ACB, and sin(angle ACB) is equal to 3.0/5.0?\nLet's think step by step and output the final answer within \\boxed{}.",
"role": "user"
... | MATH | {
"ground_truth": "10m",
"style": "rule"
} | {
"difficulty": "1",
"index": "025788f5-c0a7-480c-9718-cdecb9017ec3"
} | |
multimodal_opensource_math | [
{
"content": "<image>What is the measure of angle CAB if in the figure, angle C in parallelogram APBC is 40.0 degrees and circle O is tangent to PA and PB at points A and B?\nLet's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | MATH | {
"ground_truth": "70°",
"style": "rule"
} | {
"difficulty": "1",
"index": "07416481-6ca8-4656-abd4-43926039182f"
} | |
multimodal_opensource_math | [
{
"content": "<image>If the length of the AD side is 21, the length of the BC side is 13, the length of the AB side is 18 and the length of the CD side is 21, compute the perimeter of the ABCD trapezoid. Round computations to 2 decimal places.\nLet's think step by step and output the final answer within \\boxed... | MATH | {
"ground_truth": "73",
"style": "rule"
} | {
"difficulty": "1",
"index": "d00caf85-4fd2-4511-92b6-be766b244d7c"
} | |
multimodal_opensource_math | [
{
"content": "<image>In the given diagram, lines a and b are depicted as parallel. If angle 2 and angle 3 are equal in measure and angle 1 measures 30 degrees, what is the degree measurement of angle 4?\nLet's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | MATH | {
"ground_truth": "60°",
"style": "rule"
} | {
"difficulty": "1",
"index": "19b7b4d4-7b40-4ad7-9b85-61a2ccb62f07"
} | |
multimodal_opensource_math | [
{
"content": "<image>Consider triangle PQR, where line ST is parallel to side PQ and intersects side PR at point S and side QR at point T. If PS = 3.0, SR = 6.0, what is the ratio of length of line QT to line TR?\nLet's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | MATH | {
"ground_truth": "\\frac{1}{3}",
"style": "rule"
} | {
"difficulty": "1",
"index": "e57e313a-1de7-44c2-bd1e-c305841b46e2"
} | |
multimodal_opensource_math | [
{
"content": "<image>If point B lies on AC in circle O and the measure of angle AOC is 100 degrees, what is the degree measure of angle ABC?\nLet's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | MATH | {
"ground_truth": "130°",
"style": "rule"
} | {
"difficulty": "1",
"index": "00ff94f9-fc13-4b6d-aa92-504350f97639"
} |
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