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>Consider the given figure with tangent PA and circle O touching at point A, where PO intersects circle O at point C, and point B lies on the major arc CBA. If angle P is represented by the variable 'x' degrees, determine the degree measure of angle ABC\nLet's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "32°",
"style": "rule"
}
|
{
"difficulty": "1",
"index": "56feb64b-869a-46e8-9ebb-bfae57a5c764"
}
|
|
multimodal_opensource_math
|
[
{
"content": "<image>In the diagram, the measure of the angle LER is equal to 66 degrees. What is the measure of angle EFN?\nLet's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "114 degrees",
"style": "rule"
}
|
{
"difficulty": "1",
"index": "aa28ca22-ee30-4675-bfb4-692c4225db35"
}
|
|
multimodal_opensource_math
|
[
{
"content": "<image>If the length of the height perpendicular to the base marked with \"?\" in the gray triangle is 25 and the area of the gray triangle is 64, compute the length of the side of the gray triangle 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": "5.12",
"style": "rule"
}
|
{
"difficulty": "1",
"index": "6884436b-9c34-40a7-89b9-99cf9398a563"
}
|
|
multimodal_opensource_math
|
[
{
"content": "<image>Given that line 'a' is parallel to line 'b' in the figure, with angle 1 measuring 85.0 degrees and angle 2 measuring 35.0 degrees, what is the degree measure of angle 3?\nLet's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "50°",
"style": "rule"
}
|
{
"difficulty": "1",
"index": "cb733348-896f-429d-8bcb-3e1bf34ae5d9"
}
|
|
multimodal_opensource_math
|
[
{
"content": "<image>Utilize the concept of similar triangles to determine the length of MN. Using the proportionality of sides in similar triangles, we get \\(\\frac{OP}{PN}=\\frac{RS}{MN}\\). Substituting the given values, we find \\(\\frac{5}{5+10}=\\frac{4}{MN}\\). Solving for MN gives MN = 12. Thus, the length of MN is 12. Therefore, the answer is option B\nLet's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "12",
"style": "rule"
}
|
{
"difficulty": "1",
"index": "32971cda-f8f0-428e-842b-94182bacfd90"
}
|
|
multimodal_opensource_math
|
[
{
"content": "<image>There is a square in the diagram, represented by the symbol UOEB. OG is the extension line of UO. Line OE is perpendicular to line EB. There is a triangle MKA. The measure of angle KMA is equal to 40 degrees. What is the sum of the measures of the other two angles in triangle MKA?\nLet's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "140 degrees",
"style": "rule"
}
|
{
"difficulty": "1",
"index": "cde9118b-fd96-4d34-a4a9-1830c33c70dd"
}
|
|
multimodal_opensource_math
|
[
{
"content": "<image>In the diagram, there is a circle V with angles DVF = 65 degrees and FVB = 142 degrees. What is the measure of angle BVD?\nLet's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "153 degrees",
"style": "rule"
}
|
{
"difficulty": "1",
"index": "9e44489e-7a0c-4f7e-b9a6-2cf4d3d7bd97"
}
|
|
multimodal_opensource_math
|
[
{
"content": "<image>What is the measure of angle AOB in circle O, where chord AC intersects radius OB at point D, and angle B measures 60 degrees while angle ADB measures 116 degrees?\nLet's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "112°",
"style": "rule"
}
|
{
"difficulty": "1",
"index": "184f3037-5b04-421f-bcc4-48dcf80fdff5"
}
|
|
multimodal_opensource_math
|
[
{
"content": "<image>Given that three straight lines intersect at point O in the figure, what is the sum of angle 1, angle 2, and angle 3 in terms of their degree measures?\nLet's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "180°",
"style": "rule"
}
|
{
"difficulty": "1",
"index": "b10795af-27fa-47d2-8b17-a96c72b65152"
}
|
|
multimodal_opensource_math
|
[
{
"content": "<image>In the diagram, there is a circle F. There are lines FW, FI, FY in the diagram. Point W, Point I, and Point Y lie on the circle F. Which lines are equal in length to line FW?\nLet's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "FI, FY",
"style": "rule"
}
|
{
"difficulty": "1",
"index": "90ce29a0-dec6-4371-8e7a-93e09a0860c8"
}
|
|
multimodal_opensource_math
|
[
{
"content": "<image>Given an isosceles trapezoid representing the cross section of the railway subgrade, if the slope of the waist is expressed as a ratio i = m:n, the top width is denoted as w = 7.0 units, and the subgrade height is h = 6.0 units, determine the bottom width of the subgrade in terms of m and n\nLet's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "15米",
"style": "rule"
}
|
{
"difficulty": "1",
"index": "d1eb3e58-370c-40fd-9d2c-bd7b351d0ef3"
}
|
|
multimodal_opensource_math
|
[
{
"content": "<image>In the provided diagram, line a is parallel to line b. Line l intersects lines a and b at points A and B respectively. The perpendicular line to line l passing through point A intersects line b at point C. Let's denote angle 1 as variable u, where u = 32°. What is the degree measure of angle 2, expressed as variable v in relation to u?\nLet's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "58°",
"style": "rule"
}
|
{
"difficulty": "1",
"index": "bb6e3238-2bb6-45bb-a525-0f12e48c63a8"
}
|
|
multimodal_opensource_math
|
[
{
"content": "<image>When line c intersects lines a and b in the given diagram, with line a parallel to line b, what is the degree measure of angle 2 when angle 1 measures 55 degrees?\nLet's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "125°",
"style": "rule"
}
|
{
"difficulty": "1",
"index": "80ee3ed4-837c-4934-b301-bdb493c7de30"
}
|
|
multimodal_opensource_math
|
[
{
"content": "<image>Line MJ is the line connecting point M and the midpoint J of line TW. What is the length of line JT if the length of line TW is 14?\nLet's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "7",
"style": "rule"
}
|
{
"difficulty": "1",
"index": "4fa40e00-9b35-4e82-a165-2a9335934660"
}
|
|
multimodal_opensource_math
|
[
{
"content": "<image>If the diagonal of the ABCD rectangle is 25, the ABEF shape is a rectangle where a semi-circle has been removed from one side of it and the perimeter of the ABEF shape is 66, compute the length of the AD side of the ABCD rectangle. 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": "16.41",
"style": "rule"
}
|
{
"difficulty": "1",
"index": "bbb221c1-b7a8-46ad-81d1-19ea1ea0a19a"
}
|
|
multimodal_opensource_math
|
[
{
"content": "<image>Given that M and N are points on AB and AC respectively, and MN is parallel to BC, if the ratio of AN to AC is 0.8 and AB is 100, what is the length of AM?\nLet's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "80.0",
"style": "rule"
}
|
{
"difficulty": "1",
"index": "4d371621-5dd2-4dc5-916f-c00dacd410ae"
}
|
|
multimodal_opensource_math
|
[
{
"content": "<image>There is a parallelogram in the diagram, represented by the symbol UYRT. Which lines are equal in length to line UT?\nLet's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "YR",
"style": "rule"
}
|
{
"difficulty": "1",
"index": "107d47a5-6382-4558-a2ac-de11e5afd4d5"
}
|
|
multimodal_opensource_math
|
[
{
"content": "<image>In the figure, in quadrilateral ABCD, AC and BD intersect at point O, with OE perpendicular to BD and intersecting AD at point E. If the perimeter of quadrilateral ABCD is 20, what is the perimeter of triangle ABE?\nLet's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "10",
"style": "rule"
}
|
{
"difficulty": "1",
"index": "d280f0f3-bbf5-4da1-802d-41f9d2f53367"
}
|
|
multimodal_opensource_math
|
[
{
"content": "<image>There is a rectangle in the diagram, represented by the symbol DHUL. What is the length of line DL?\nLet's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "5",
"style": "rule"
}
|
{
"difficulty": "1",
"index": "c60d555c-5237-408c-885a-9d75cfe08482"
}
|
|
multimodal_opensource_math
|
[
{
"content": "<image>There is a pentagon in the diagram, represented by the symbol KFGXV. What is the sum of the interior angles of this pentagon?\nLet's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "540 degrees",
"style": "rule"
}
|
{
"difficulty": "1",
"index": "e83732b9-e174-47d1-9492-42ac92f3e35e"
}
|
|
multimodal_opensource_math
|
[
{
"content": "<image>As shown in the figure, AB is the chord of circle O, CD is tangent to circle O at point A, if angle BAD = 66.0, then angle B is equal to ()\nLet's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "24°",
"style": "rule"
}
|
{
"difficulty": "1",
"index": "872f486d-0dae-42c2-88bb-ad6eda0327e0"
}
|
|
multimodal_opensource_math
|
[
{
"content": "<image>In triangle ABC, let's represent angle A as variable u where u = 20°. If line BD is both perpendicular to and bisects line AC, what is the degree measure of angle CBD, expressed as variable v in relation to u?\nLet's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "70°",
"style": "rule"
}
|
{
"difficulty": "1",
"index": "de35a872-adce-48a2-b719-04175bea8b81"
}
|
|
multimodal_opensource_math
|
[
{
"content": "<image>Line RH is the line connecting the midpoint R of line ZB and the midpoint H of line PC. What is the length of line RZ if the length of line ZB is 8?\nLet's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "4",
"style": "rule"
}
|
{
"difficulty": "1",
"index": "3927a20d-8fdd-4535-99da-642d26af8233"
}
|
|
multimodal_opensource_math
|
[
{
"content": "<image>In the provided diagram, let's denote the central angle BOC as variable u where u = 40.0 degrees. If AB is the diameter of circle O and arcs BC, CD, and DE are congruent, what is the degree measure of angle AOE, expressed as variable v in relation to u?\nLet's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "60°",
"style": "rule"
}
|
{
"difficulty": "1",
"index": "94fb15b8-4047-4e13-9b8b-67e957c3c074"
}
|
|
multimodal_opensource_math
|
[
{
"content": "<image>In the given diagram, Xiao Liang begins his journey from point A and moves forward a distance of 10.0 units. He then makes a right turn and moves 15.0 units. Afterwards, he moves forward again for 10.0 units and makes another right turn of 15.0 units. As he finally returns to the starting point A, what is the total distance he has walked?\nLet's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "240米",
"style": "rule"
}
|
{
"difficulty": "1",
"index": "fbc34d6e-6669-4c81-9bd6-60ea8aead5d7"
}
|
|
multimodal_opensource_math
|
[
{
"content": "<image>In triangle ABC, point D and point E are respectively the midpoints of the sides AB and AC. Point G is the midpoint of EC, and DG intersects the extended line of BC at point F. If the area of triangle GCF is represented by variable x and equals 2, what is the area of triangle ABC, expressed as variable y in terms of x?\nLet's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "16",
"style": "rule"
}
|
{
"difficulty": "1",
"index": "d06de71c-b848-44ca-a22a-a00642167af5"
}
|
|
multimodal_opensource_math
|
[
{
"content": "<image>In the provided figure, AB and CD both measure 10.0 in length, and the arcs BC and DA have the same arc length and radius. What is the area of the shaded part relative to the square of its measure?\nLet's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "100",
"style": "rule"
}
|
{
"difficulty": "1",
"index": "4de012d0-4e3b-4adb-aa78-cf9f120abac3"
}
|
|
multimodal_opensource_math
|
[
{
"content": "<image>There is a regular pentagon in the diagram, represented by the symbol LMFHQ. The length of line HQ is 15. What is the length of line LM?\nLet's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "15",
"style": "rule"
}
|
{
"difficulty": "1",
"index": "e8b40775-ceca-4a52-96ee-81ec3863b903"
}
|
|
multimodal_opensource_math
|
[
{
"content": "<image>In the given figure, C and D are two points on the line segment AB, and D is the midpoint of the line segment AC. If AB is 40 units long and BC is 16 units long, what is the length of AD?\nLet's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "12.0",
"style": "rule"
}
|
{
"difficulty": "1",
"index": "9af72a55-96c9-4f37-99f1-45ebf87fb64f"
}
|
|
multimodal_opensource_math
|
[
{
"content": "<image>In the diagram, there is a circle T. There are lines TM, CA, LK in the diagram. Point M, Point C, Point A, Point L, and Point K lie on the circle T. Which lines are equal in length to line TM?\nLet's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "TC, TA, TL, TK",
"style": "rule"
}
|
{
"difficulty": "1",
"index": "a35b261c-041c-4af0-9759-890f1ec6af45"
}
|
|
multimodal_opensource_math
|
[
{
"content": "<image>In the diagram representing square ABCD, we can see that point E lies on diagonal BD, such that the length of segment BE is equivalent to the length of segment AB. If we draw segments CE and AE, what will be the value of angle DAE, in degrees?\nLet's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "22.5°",
"style": "rule"
}
|
{
"difficulty": "1",
"index": "76fbf115-8271-43fd-9df7-e312e28fa16b"
}
|
|
multimodal_opensource_math
|
[
{
"content": "<image>If AB measures 8.0 and BC measures 12.0 in the parallelogram ABCD shown in the figure, and the perpendicular bisector of AC intersects AD at point E, what is the perimeter of triangle CDE?\nLet's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "20",
"style": "rule"
}
|
{
"difficulty": "1",
"index": "98cb6bf7-ec7c-44df-b4a6-5fda025d4be8"
}
|
|
multimodal_opensource_math
|
[
{
"content": "<image>If DE is parallel to BC and BE divides angle ABC into two equal angles, what is the measure of angle CBE in degrees, given that angle 1 has a measure of 66°?\nLet's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "33°",
"style": "rule"
}
|
{
"difficulty": "1",
"index": "26554ba6-e5b1-4de0-b57c-175446924227"
}
|
|
multimodal_opensource_math
|
[
{
"content": "<image>In triangle ABC, points D and E are the midpoints of sides AB and AC respectively. If the length of DE is represented by the variable 'd', what is the length of BC?\nLet's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "6",
"style": "rule"
}
|
{
"difficulty": "1",
"index": "b25f6ff4-d2f2-4c58-ad75-a5690acdd58c"
}
|
|
multimodal_opensource_math
|
[
{
"content": "<image>Consider the diagram where quadrilateral ABCD is inscribed in circle O, with AB as the diameter of circle O and EC tangent to circle O at point C, and angle ECB equal to 35.0 degrees. What is the measure of angle D in degrees?\nLet's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "125°",
"style": "rule"
}
|
{
"difficulty": "1",
"index": "08583fe6-a7d0-47fe-bcae-299105dcd16a"
}
|
|
multimodal_opensource_math
|
[
{
"content": "<image>In the figure provided, if point A serves as the center of circle O with a radius of 3.0 units, and an arc is drawn with OA as the radius to intersect circle O at points B and C, what will be the measure of BC?\nLet's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "3√{3}",
"style": "rule"
}
|
{
"difficulty": "1",
"index": "37cd1746-5ea9-4a34-91da-9338199b020e"
}
|
|
multimodal_opensource_math
|
[
{
"content": "<image>In the given figure, the diagonals of parallelogram ABCD intersect at point 0.0. The line OM is perpendicular to AC and passes through point 0.0. It intersects AD at point M. If the perimeter of triangle CDM measures 5.0, what is the perimeter of parallelogram ABCD?\nLet's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "10",
"style": "rule"
}
|
{
"difficulty": "1",
"index": "90f9cab9-49e9-4354-98db-fe060ba3242f"
}
|
|
multimodal_opensource_math
|
[
{
"content": "<image>In quadrilateral ABCD, let angle B be represented as x degrees and angle D be represented as y degrees. If the sum of angle B and angle D is 200°, find the measure of angle A in terms of x and y\nLet's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "80°",
"style": "rule"
}
|
{
"difficulty": "1",
"index": "d7517224-b383-4260-b4d3-ecb0cc95ac3f"
}
|
|
multimodal_opensource_math
|
[
{
"content": "<image>After a semicircle with AB as its diameter and a length of 4.0 units rotates clockwise around point B by 45.0 degrees, leading point A to move to A′, what is the area of the shaded part in the figure?\nLet's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "2π",
"style": "rule"
}
|
{
"difficulty": "1",
"index": "54909025-b9a3-43ee-99cf-e6f711cde1cd"
}
|
|
multimodal_opensource_math
|
[
{
"content": "<image>There is a right triangle in the diagram, represented by the symbol GYW. Line GS is the line connecting point G and the midpoint S of line YW. If the length of the hypotenuse YW is 10, what is the length of line GS?\nLet's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "5",
"style": "rule"
}
|
{
"difficulty": "1",
"index": "efc7b058-4f1c-4d2e-a3b6-2f127be1e80c"
}
|
|
multimodal_opensource_math
|
[
{
"content": "<image>In the given diagram, let's denote the measure of angle EDC as variable k (k = 25.0), the measure of angle DCE as variable n (n = 25.0), and the measure of angle B as variable q (q = 70.0). If CD is the bisector of angle ACB, what is the degree measure of angle BDC, expressed as variable w using k, n, and q?\nLet's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "85°",
"style": "rule"
}
|
{
"difficulty": "1",
"index": "e4682c1d-89ae-4999-bcf9-3e62a7efa4eb"
}
|
|
multimodal_opensource_math
|
[
{
"content": "<image>If AB is parallel to CD and AD is perpendicular to CE at point A, with angle 1 measuring 60 degrees as shown in the diagram, what is the measurement of angle 2?\nLet's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "30°",
"style": "rule"
}
|
{
"difficulty": "1",
"index": "5aee23f6-977e-4979-83f5-502212c30f9e"
}
|
|
multimodal_opensource_math
|
[
{
"content": "<image>When triangle ABC is rotated clockwise by 120.0 degrees around point A to form triangle ADE in the provided figure, where the corresponding points are B and E, and C and D respectively, and if the measure of angle BAC is 35.0 degrees, what is the degree measure of angle CAE in triangle ADE?\nLet's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "85°",
"style": "rule"
}
|
{
"difficulty": "1",
"index": "5d3dbc63-605a-4868-abdc-439ae780b782"
}
|
|
multimodal_opensource_math
|
[
{
"content": "<image>Given the roof truss design, where point D is positioned as the midpoint of the diagonal beam labeled as AB, and with the columns BC and DE being perpendicular to the cross beam denoted as AC, find the length of DE, represented as 'z' units, in terms of AB, denoted by 'x' units\nLet's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "2m",
"style": "rule"
}
|
{
"difficulty": "1",
"index": "ecd7c5c7-b6e0-4181-8c79-7e217c45b095"
}
|
|
multimodal_opensource_math
|
[
{
"content": "<image>In the given figure, if AD is 6cm and AB is 4cm, what is the perimeter of quadrilateral ABCD?\nLet's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "20cm",
"style": "rule"
}
|
{
"difficulty": "1",
"index": "a4d79828-7f3c-44b2-8f96-d2031f1e30d3"
}
|
|
multimodal_opensource_math
|
[
{
"content": "<image>As shown in the figure, rotate triangle AOB around point O by 45.0 counterclockwise to get triangle A′OB′, if triangle AOB = 15.0, then the degree of angle AOB′ is ()\nLet's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "30°",
"style": "rule"
}
|
{
"difficulty": "1",
"index": "2183769c-8771-45aa-af98-aaf5dad85567"
}
|
|
multimodal_opensource_math
|
[
{
"content": "<image>In the diagram, there is a circle T. The line OZ passes through the center of the circle T at point T and is the diameter of the circle. Which lines are equal in length to line OT?\nLet's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "TZ",
"style": "rule"
}
|
{
"difficulty": "1",
"index": "010101a0-dcb8-4e13-b9ae-f81af298a653"
}
|
|
multimodal_opensource_math
|
[
{
"content": "<image>In the figure, a right triangle ABC with ∠BAC measuring 60.0 is rotated clockwise by 45.0 around vertex A to create triangle AB′C′. The path of point B is arc BB′. If AC measures 1.0 and ∠BAC is 60.0, what is the area of the shaded region in the figure?\nLet's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "\\frac{π}{2}",
"style": "rule"
}
|
{
"difficulty": "1",
"index": "60c650b7-deb1-4e53-a27e-7817b371f790"
}
|
|
multimodal_opensource_math
|
[
{
"content": "<image>There is a triangle OJF. The measure of angle JOF is 70 degrees. What is the sum of the measures of angles OJF and FJO?\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": "3ef5fe43-a7be-495f-ad8f-61192818d6b9"
}
|
|
multimodal_opensource_math
|
[
{
"content": "<image>There is a hexagon in the diagram, represented by the symbol CRMIOB. Which two angles are right angles?\nLet's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "angles BCR and CRM",
"style": "rule"
}
|
{
"difficulty": "1",
"index": "c1da49ed-43f1-4760-b5fe-02e0113babd7"
}
|
|
multimodal_opensource_math
|
[
{
"content": "<image>Known: As shown in the figure, in the inscribed quadrilateral ABCD of circle O, AB is the diameter, angle BCD = 130.0, the tangent PD passing through the point D and the straight line AB intersect at the point P, then the degree of angle ADP is ()\nLet's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "40°",
"style": "rule"
}
|
{
"difficulty": "1",
"index": "0e8d5fdd-3233-446f-b749-e5b076c7ca3d"
}
|
|
multimodal_opensource_math
|
[
{
"content": "<image>In triangle ABC, where the length of BC is represented by variable u (u = 6), D and E are the midpoints of BC and AC respectively. BF bisects angle ABC and intersects DE at point F. What is the length of DF, expressed as variable v in relation to u?\nLet's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "3",
"style": "rule"
}
|
{
"difficulty": "1",
"index": "d9e4bb59-2814-4b05-9476-52e134893978"
}
|
|
multimodal_opensource_math
|
[
{
"content": "<image>How many gray cylinders were subtracted if there is 1 gray cylinder left?\nLet's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "2",
"style": "rule"
}
|
{
"difficulty": "1",
"index": "a4a2395b-4f09-4cc7-8e19-ae32fd6284a6"
}
|
|
multimodal_opensource_math
|
[
{
"content": "<image>Given a triangle ABC with vertices A, B, and C on circle O, what is the measure of angle AOC if angle ABC measures 28.0 degrees?\nLet's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "56°",
"style": "rule"
}
|
{
"difficulty": "1",
"index": "780cefaf-a301-4091-a2e1-a6d643b9b64e"
}
|
|
multimodal_opensource_math
|
[
{
"content": "<image>There is a quadrilateral NMUJ. Which points of this quadrilateral lie on the hexagon ETPOSC?\nLet's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "N, M, U, J",
"style": "rule"
}
|
{
"difficulty": "1",
"index": "d4c00662-2323-446f-8998-e5896574db35"
}
|
|
multimodal_opensource_math
|
[
{
"content": "<image>In a flower and tree farm, an open space is shaped like an isosceles trapezoid ABCD, with E, F, G, and H as the midpoints of each side. The diagonal AC is measured at 10.0. When creating a quadrilateral EFGH field using a fence, how long does the fence need to be?\nLet's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "20米",
"style": "rule"
}
|
{
"difficulty": "1",
"index": "55db02fd-5b23-4a73-abea-6e2e6bff5211"
}
|
|
multimodal_opensource_math
|
[
{
"content": "<image>If the arc length of the brown sector is 15.42, compute the degree of the angle marked with question mark. 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": "46.8",
"style": "rule"
}
|
{
"difficulty": "1",
"index": "6bfbb142-1e0e-4603-b965-053c002d10e5"
}
|
|
multimodal_opensource_math
|
[
{
"content": "<image>Consider a parallelogram WXYZ, where side WX measures 'x' units and side WY measures 'y' units. The angle bisector of angle WXY intersects side WZ at point M and extends to intersect the extended line of YZ at point N. What is the length of segment MN?\nLet's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "3cm",
"style": "rule"
}
|
{
"difficulty": "1",
"index": "b99268a9-e2ac-463a-95c3-9b444c13a897"
}
|
|
multimodal_opensource_math
|
[
{
"content": "<image>Suppose we have triangle ABC with angle BAC measuring 30 degrees and both sides AB and AC measuring 12 units. As a point P moves along side AB, a parallelogram PAQC is formed. Determine the minimum length of diagonal PQ in this situation\nLet's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "6",
"style": "rule"
}
|
{
"difficulty": "1",
"index": "0711ae8b-e6cb-435e-bc96-e83434ca5f7a"
}
|
|
multimodal_opensource_math
|
[
{
"content": "<image>As depicted in the figure, AC serves as the diameter of circle O, with chord AB being parallel to CD. If the measure of angle BAC is determined to be 32.0 degrees, what will be the measure of angle AOD?\nLet's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "64°",
"style": "rule"
}
|
{
"difficulty": "1",
"index": "ab0eb5a8-d36f-4fd9-aa4f-95b85338bb9c"
}
|
|
multimodal_opensource_math
|
[
{
"content": "<image>In triangle ABC, let angle A be represented by the variable x (x = 30°). E is a point on the extension of BC. The angle bisector of angle ABC and angle ACE intersect at point D. What is the measure of angle D, expressed as variable y in terms of x?\nLet's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "15°",
"style": "rule"
}
|
{
"difficulty": "1",
"index": "f212aeaf-6e62-46c7-9866-288bc99c48e0"
}
|
|
multimodal_opensource_math
|
[
{
"content": "<image>Line ZF is perpendicular to line HF. What is the angle between ZF and HF?\nLet's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "90 degrees",
"style": "rule"
}
|
{
"difficulty": "1",
"index": "05cabf3c-c897-457f-8708-768fff05d68a"
}
|
|
multimodal_opensource_math
|
[
{
"content": "<image>In the provided diagram of circle O, let's denote the angles A, APD, and D as variables u, v, and w respectively (u = 42.0, v = 77.0). What is the degree measure of angle B, expressed as variable x in relation to u, v, and w?\nLet's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "35°",
"style": "rule"
}
|
{
"difficulty": "1",
"index": "04ebdc9e-9283-43d0-9100-efdb0832133b"
}
|
|
multimodal_opensource_math
|
[
{
"content": "<image>There is also a rectangle in the diagram, represented by the symbol YIZS. If the length of line IZ is 10, what is the length of SY?\nLet's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "10",
"style": "rule"
}
|
{
"difficulty": "1",
"index": "9ba34b61-a64b-449a-94e8-7fc970393d9d"
}
|
|
multimodal_opensource_math
|
[
{
"content": "<image>In the given diagram, let's represent the angle of rotation of line l around point E as variable h, where h = 40.0°. Line l intersects line AB at point G after the rotation. If the measure of angle GEC is represented by variable k, where k = 80.0°, what is the numerical value of angle GFE, expressed as variable n in relation to h and k?\nLet's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "60°",
"style": "rule"
}
|
{
"difficulty": "1",
"index": "33313da4-ad06-422c-857c-a4db3ef39195"
}
|
|
multimodal_opensource_math
|
[
{
"content": "<image>In the provided figure, let's represent the minimum rotation of l1 around point O as variable y. What is the value of y required to make l1 parallel to l2?\nLet's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "38°",
"style": "rule"
}
|
{
"difficulty": "1",
"index": "a78e4d26-eb3a-4e90-8f37-eae2d291399e"
}
|
|
multimodal_opensource_math
|
[
{
"content": "<image>In the diagram, there is a circle F with diameters JN and ET. What is the length of these diameters if the radius of the circle is 3.0?\nLet's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "6.0",
"style": "rule"
}
|
{
"difficulty": "1",
"index": "8e6b3fdb-4593-49af-a11c-9317aecbab73"
}
|
|
multimodal_opensource_math
|
[
{
"content": "<image>In triangle ABC, where AB = a and AC = b, a straight line DE is drawn parallel to CB passing through point A. The line DE intersects the bisector of angle ABC and angle ACB at points E and D, respectively. What is the length of DE expressed in terms of a and b?\nLet's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "13",
"style": "rule"
}
|
{
"difficulty": "1",
"index": "6f771070-cd77-4ef0-ac60-b05ce01957d1"
}
|
|
multimodal_opensource_math
|
[
{
"content": "<image>Let's examine the square RSVP, with point E located on its diagonal. The quadrilateral EFCD is a rectangle. Express the sum of the lengths of EG and CD in terms of the side length 'a' of square RSVP\nLet's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "4",
"style": "rule"
}
|
{
"difficulty": "1",
"index": "e74e779e-e971-49c0-850f-4502f6405d3f"
}
|
|
multimodal_opensource_math
|
[
{
"content": "<image>Is the left graph isomorphic with the right graph?\nLet's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "No",
"style": "rule"
}
|
{
"difficulty": "1",
"index": "ae0f2338-1c5d-4389-af80-8af411642e2a"
}
|
|
multimodal_opensource_math
|
[
{
"content": "<image>How many total shapes are left after removing all red cylinders and counting the remaining spheres and cubes?\nLet's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "6",
"style": "rule"
}
|
{
"difficulty": "1",
"index": "df53aaf8-44d9-4237-b55c-43677f36871e"
}
|
|
multimodal_opensource_math
|
[
{
"content": "<image>In the diagram, there is a circle S with points X, E, and O lying on the circle. Which lines are equal in length to line SX?\nLet's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "SE, SO",
"style": "rule"
}
|
{
"difficulty": "1",
"index": "6f01a637-3949-4223-9ef1-30fe9fc4a7ee"
}
|
|
multimodal_opensource_math
|
[
{
"content": "<image>There is a hexagon in the diagram, represented by the symbol ZOBAWN. How many sides does this hexagon have?\nLet's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "six",
"style": "rule"
}
|
{
"difficulty": "1",
"index": "0bcf7f3b-ff28-4637-8296-95906da0c559"
}
|
|
multimodal_opensource_math
|
[
{
"content": "<image>In triangle ABC, as illustrated, D and E denote the midpoints of AC and AB respectively. If the area of triangle ABC is 12, what is the area of triangle BDE?\nLet's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "3",
"style": "rule"
}
|
{
"difficulty": "1",
"index": "79aaa265-d4a3-4dc6-97b9-0672a3095fa6"
}
|
|
multimodal_opensource_math
|
[
{
"content": "<image>What is the length of line IE in the rhombus IELC?\nLet's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "11",
"style": "rule"
}
|
{
"difficulty": "1",
"index": "76599db3-77a9-4448-9080-d0f4aebac524"
}
|
|
multimodal_opensource_math
|
[
{
"content": "<image>There is a line YA. What is the length of line AZ if the length of line ZV is 11?\nLet's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "5.5",
"style": "rule"
}
|
{
"difficulty": "1",
"index": "c4c5b4d6-26a5-41d2-8e78-b1c75ddf58e4"
}
|
|
multimodal_opensource_math
|
[
{
"content": "<image>According to the given figure, Xiaochao, whose height is 1.8 units, stands beneath a street lamp. Upon observing his shadow, he realizes that it spans exactly 3.0 units. Additional measurements show that the distance between Xiaochao and the base of the street lamp measures 9.0 units. What conclusions can you draw about the height of the street lamp from the ground?\nLet's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "7.2m",
"style": "rule"
}
|
{
"difficulty": "1",
"index": "a55c34c4-61a5-4800-a1c1-d34a7803d3b8"
}
|
|
multimodal_opensource_math
|
[
{
"content": "<image>如图所示，在Rt△ABC中，∠A=25°，∠ACB=90°，以点C为圆心，BC为半径的圆交AB于一点D，交AC于点E，则∠DCE的度数是多少？\nLet's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "40°",
"style": "rule"
}
|
{
"difficulty": "1",
"index": "ee268c77-70eb-46bd-8ce4-93f2d09cf894"
}
|
|
multimodal_opensource_math
|
[
{
"content": "<image>In the diagram, there is a circle B with a radius of 0.4. What is the circumference of the circle B? Approximating π≈3.14.\nLet's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "2.512",
"style": "rule"
}
|
{
"difficulty": "1",
"index": "f0068541-0e16-40ab-9acf-905d600beb41"
}
|
|
multimodal_opensource_math
|
[
{
"content": "<image>What is the measure of \\angle{ABF} if m\\angle{ABD} = x + 14 and x = 36?\nLet's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "100 degrees",
"style": "rule"
}
|
{
"difficulty": "1",
"index": "cb93a975-b8fb-4299-a306-1f99775f404e"
}
|
|
multimodal_opensource_math
|
[
{
"content": "<image>In the diagram, the measure of the angle HZA is equal to 117 degrees and the measure of the angle WAM is equal to 117 degrees. Are the lines HY and WQ parallel?\nLet's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "yes",
"style": "rule"
}
|
{
"difficulty": "1",
"index": "c7d996b1-a05d-42a7-b766-271b5d359985"
}
|
|
multimodal_opensource_math
|
[
{
"content": "<image>Find the perimeter of orange square.\nLet's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "24",
"style": "rule"
}
|
{
"difficulty": "1",
"index": "8dc8964f-bfc5-42cb-bdef-52c44282e500"
}
|
|
multimodal_opensource_math
|
[
{
"content": "<image>In the given triangle ABC, if the angle C is represented by the variable h (h = 90.0 degrees), the length of side BC is represented by the variable u (u = 2.0), and the length of side AB is represented by the variable v (v = 3.0), what is the value of cosB, expressed as variable x in terms of h, u, and v?\nLet's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "\\frac{2}{3}",
"style": "rule"
}
|
{
"difficulty": "1",
"index": "2c682ab7-125e-460a-bd03-bfe3f09983ff"
}
|
|
multimodal_opensource_math
|
[
{
"content": "<image>As shown in the figure, it is known that the area of the sector of the unfolded cone's lateral surface is 65π cm2 and the arc length of the sector is 13π cm. The length of the cone's generatrix is ()\nLet's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "10cm",
"style": "rule"
}
|
{
"difficulty": "1",
"index": "a32c69f2-8523-4055-92d5-af1dd68028bc"
}
|
|
multimodal_opensource_math
|
[
{
"content": "<image>In the provided diagram, angle BAC is represented by variable u (u = 40.0 degrees), angle ADG is represented by variable v (v = 130.0 degrees), and angle DGF is represented by variable w. What is the numerical value of w in relation to u and v?\nLet's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "150°",
"style": "rule"
}
|
{
"difficulty": "1",
"index": "82fd6ddc-c85e-4a23-a8a5-ba35f77351da"
}
|
|
multimodal_opensource_math
|
[
{
"content": "<image>In the diagram, the length of the radius HG is given as 2.8. What is the diameter of the circle H?\nLet's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "5.6",
"style": "rule"
}
|
{
"difficulty": "1",
"index": "03d5864b-aadc-4582-b979-2131748d3a8a"
}
|
|
multimodal_opensource_math
|
[
{
"content": "<image>In triangle ABC as depicted in the figure, with line DE parallel to side BC, and with the ratio of AD to DB established as 1.0 to 3.0, and with BC measuring 8.0 units, what is the length of DE?\nLet's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "2",
"style": "rule"
}
|
{
"difficulty": "1",
"index": "2553c591-aa85-4b13-a480-e569a1276c50"
}
|
|
multimodal_opensource_math
|
[
{
"content": "<image>In circle O, where BC serves as the diameter and A and D are points on the circle, if the measure of angle D is denoted by the symbol 'alpha', what is the measure of angle OAC in terms of 'alpha'?\nLet's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "55°",
"style": "rule"
}
|
{
"difficulty": "1",
"index": "312bdb30-61cb-4ad6-9200-62ddbbadc373"
}
|
|
multimodal_opensource_math
|
[
{
"content": "<image>According to the diagram, line AB is parallel to line CD, and EF acts as an angle bisector for angle BEG. If angle 1 is measured at 50 degrees, what is the degree measure of angle 2?\nLet's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "65°",
"style": "rule"
}
|
{
"difficulty": "1",
"index": "543ab6c3-b4f4-4e68-86ee-e61e5ad33774"
}
|
|
multimodal_opensource_math
|
[
{
"content": "<image>In parallelogram ABCD, where AB = 6.0 and AD = 9.0, the bisector of angle BAD intersects BC at point E. The extension of DC intersects at point F, with EF = 2.0. Find the perimeter of triangle CEF\nLet's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "8",
"style": "rule"
}
|
{
"difficulty": "1",
"index": "443e5989-caf0-44f5-a2ea-c413e348f337"
}
|
|
multimodal_opensource_math
|
[
{
"content": "<image>If the side length of square JETS is doubled, what will be the new area of quadrilateral ABCD?\nLet's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "36",
"style": "rule"
}
|
{
"difficulty": "1",
"index": "40600bd0-b450-4e5d-b509-4f19293df824"
}
|
|
multimodal_opensource_math
|
[
{
"content": "<image>When OC is perpendicular to AB and points A, B, C, D, and P are located on circle O, and angle ADC measures 15° (where 0° < α < 90°), what is the measure of angle APB?\nLet's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "150°",
"style": "rule"
}
|
{
"difficulty": "1",
"index": "ce669aab-6af0-49b9-babf-310269288cdd"
}
|
|
multimodal_opensource_math
|
[
{
"content": "<image>如图,四边形ABCD内接于⊙O,若∠A=50°,则∠C的度数是多少？\nLet's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "130°",
"style": "rule"
}
|
{
"difficulty": "1",
"index": "9dd7d351-9f44-4358-9b7c-9c5d00c9bc66"
}
|
|
multimodal_opensource_math
|
[
{
"content": "<image>There is a triangle RVF. The measure of angle VRF is equal to 38 degrees. What is the sum of the measures of the other two angles of the triangle?\nLet's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "142 degrees",
"style": "rule"
}
|
{
"difficulty": "1",
"index": "1b9de986-8b63-4077-b0af-0bf4e76edb0a"
}
|
|
multimodal_opensource_math
|
[
{
"content": "<image>In the given diagram, let's denote the length of AB as variable x, the length of BC as variable y, and the length of DE as variable z. If AB = 13cm, BC = 10cm, and DE = 5cm, what is the area of the shaded part in the diagram? Express the area as variable S_shaded in terms of x, y, and z\nLet's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "30",
"style": "rule"
}
|
{
"difficulty": "1",
"index": "c619066b-a917-4187-9db0-d64d1af9ba72"
}
|
|
multimodal_opensource_math
|
[
{
"content": "<image>如图,在⊙O中,∠BOC=60°,则∠BAC等于()\nLet's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "30°",
"style": "rule"
}
|
{
"difficulty": "1",
"index": "60c05cb2-d5f6-4f7e-b454-1ef9996fdae2"
}
|
|
multimodal_opensource_math
|
[
{
"content": "<image>Given a parallelogram ABCD and the midpoint of CD being M, and the intersection of AM and BD being N, if the area of triangle DMN is 3.0, what is the area of triangle BAN?\nLet's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "12",
"style": "rule"
}
|
{
"difficulty": "1",
"index": "a690def5-e664-4e09-bfa8-0ebb1eadbb9c"
}
|
|
multimodal_opensource_math
|
[
{
"content": "<image>If the arc length of the cyan sector is 20.56, the angle $\\beta$ and the adjacent 50 degree angle are complementary, the angle $\\gamma$ is vertical to $\\delta$ and the angle $\\theta$ is vertical to $\\alpha$, compute the length of the side of the cyan sector marked with question mark. 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": "11.3",
"style": "rule"
}
|
{
"difficulty": "1",
"index": "dba2de91-2707-4555-ac96-1065718d3fce"
}
|
|
multimodal_opensource_math
|
[
{
"content": "<image>In the provided figure, where ABCD is a quadrilateral with a circle inscribed inside it, if angle B is measured at 50.0 degrees, what is the measure of angle D?\nLet's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "130°",
"style": "rule"
}
|
{
"difficulty": "1",
"index": "3bf54057-9d1c-422f-a471-22be356ab230"
}
|
|
multimodal_opensource_math
|
[
{
"content": "<image>Given that AE is the median of side BC of triangle ABC, where AB = x, BC = y, and the perimeter of triangle ACE is 2 more than the perimeter of triangle AEB, find the length of AC in terms of x and y\nLet's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "10",
"style": "rule"
}
|
{
"difficulty": "1",
"index": "0c1e41d6-901a-470c-b8f1-7c04539dc9d0"
}
|
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