id stringlengths 29 36 | conversations listlengths 1 48 | images listlengths 1 1 | source_dataset stringclasses 2
values |
|---|---|---|---|
vision_r1_mulberry_sft_full-195081 | [
{
"from": "user",
"value": "<image>Given a cone with a radius 'r' units and a generatrix length 'g' units, determine its lateral area. Express the lateral area as a function of 'r' and 'g'.\nChoices:\nA: 60πcm^{2}\nB: 45πcm^{2}\nC: 30πcm^{2}\nD: 15πcm^{2}"
},
{
"from": "assistant",
"value": "<th... | [
"mulberry_images/geoqa_plus/2025.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-195082 | [
{
"from": "user",
"value": "<image>In the figure, circle O has a radius of 5.0, and triangle ABC is inscribed within it with CD perpendicular to point D. If AC measures 6.0 and CD measures 3.0, what is the length of BC?\nChoices:\nA: 3\nB: 5\nC: 3√{2}\nD: 6"
},
{
"from": "assistant",
"value": "<... | [
"mulberry_images/geoqa_plus/5553.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-195083 | [
{
"from": "user",
"value": "<image>Given that the length of a slope is 130.0 and the vertical distance from the top of the slope to the horizontal ground is 50.0, what is the value of the tangent of the angle formed by the slope and the horizontal ground?\nChoices:\nA: \\frac{5}{13}\nB: \\frac{12}{13}\nC: \... | [
"mulberry_images/geoqa_plus/6799.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-195084 | [
{
"from": "user",
"value": "<image>With the aerial drone recording the elevation angle of the top B of a building from point A as 30.0 degrees, the depression angle of the bottom C as 60.0 degrees, and with a known horizontal distance AD of 90.0, what is the likely height of the building BC?\nChoices:\nA: 1... | [
"mulberry_images/geoqa_plus/8180.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-195085 | [
{
"from": "user",
"value": "<image>Consider a polygon with n sides, where a circle of radius 1.0 unit is drawn with the vertex of the polygon as the center. In the given figure, what is the total area, in square units, of the shaded region?\nChoices:\nA: πn²\nB: 2πn\nC: \\frac{1}{2}πn²\nD: π"
},
{
"... | [
"mulberry_images/geoqa_plus/6688.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-195086 | [
{
"from": "user",
"value": "<image>In the figure provided, triangle ABC is shown with angle A set at 90 degrees. On side AC lies point D, while DE runs parallel to BC. If angle 1 is known to be 145 degrees, what is the degree measure of angle B?\nChoices:\nA: 35°\nB: 25°\nC: 45°\nD: 55°"
},
{
"from"... | [
"mulberry_images/geoqa_plus/82.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-195087 | [
{
"from": "user",
"value": "<image>In the provided figure representing triangle ABC where AB is 6.0, AC is 5.0, with D as the midpoint of side AB, and E as a point on edge AC, and angle ADE equal to angle C, what is the value of the fraction AFAG if the bisector of angle BAC intersects DE and BC at points F... | [
"mulberry_images/geoqa_plus/4597.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-195088 | [
{
"from": "user",
"value": "<image>In the given figure, D and E are points on the sides AB and BC of triangle ABC, and DE is parallel to AC. The lines AE and CD intersect at point O. If the ratio of the areas of triangle DOE to triangle COA is 1:9 and the area of triangle BDE is 3, what is the area of trian... | [
"mulberry_images/geoqa_plus/4548.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-195089 | [
{
"from": "user",
"value": "<image>In the triangle ABC diagram, DE runs parallel to BC. With the ratio of AD to AB being 1:3 and DE measuring 3.0, what is the length of BC?\nChoices:\nA: 6\nB: 7\nC: 8\nD: 9"
},
{
"from": "assistant",
"value": "<think> Okay, so I've got this geometry problem here... | [
"mulberry_images/geoqa_plus/7655.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-195090 | [
{
"from": "user",
"value": "<image>In the given scenario with angle ACB at 30 degrees, CD measuring 36.0, and angle ACD equal to angle ACB, what is the height of flagpole AB where DA is perpendicular to AC at point A?\nChoices:\nA: 9m\nB: 18m\nC: 36m\nD: 72m"
},
{
"from": "assistant",
"value": "... | [
"mulberry_images/geoqa_plus/5887.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-195091 | [
{
"from": "user",
"value": "<image>When a line is drawn parallel to BC through point A in triangle ABC, where AB equals AC, and angle 1 is 65.0 degrees, what is the measure of angle BAC?\nChoices:\nA: 30°\nB: 15°\nC: 50°\nD: 70°"
},
{
"from": "assistant",
"value": "<think> Okay, let's try to fig... | [
"mulberry_images/geoqa_plus/5694.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-195092 | [
{
"from": "user",
"value": "<image>If angle 1 in the provided figure is 100.0 degrees and angle C is 70.0 degrees, what is the degree of angle A?\nChoices:\nA: 10°\nB: 20°\nC: 30°\nD: 80°"
},
{
"from": "assistant",
"value": "<think> Okay, let me try to work through this problem step by step. So,... | [
"mulberry_images/geoqa_plus/52.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-195093 | [
{
"from": "user",
"value": "<image>In the physical education class, when two students belonging to Class A and B of Grade 9 are standing at positions C and D respectively, it is observed that the shadow of student B is completely contained within the shadow of student A. What is the length of student A's sh... | [
"mulberry_images/geoqa_plus/2355.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-195094 | [
{
"from": "user",
"value": "<image>Within the given figure, there is a flat mirror marked as CD. A light ray is generated from point A and undergoes reflection at point E on CD, ultimately terminating at point B. If we assign α as the incident angle (equal to the reflection angle), and AC as perpendicular t... | [
"mulberry_images/geoqa_plus/2308.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-195095 | [
{
"from": "user",
"value": "<image>When considering the figure, where AB is a chord of circle O and OC is perpendicular to AB at point H, and the angle AOC measures 60.0 degrees with OH being 1.0, what would be the radius of circle O?\nChoices:\nA: √{3}\nB: 2\nC: 3\nD: 4"
},
{
"from": "assistant",
... | [
"mulberry_images/geoqa_plus/5203.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-195096 | [
{
"from": "user",
"value": "<image>In the figure representing a seesaw, the horizontal board AB is depicted to pivot up and down around the midpoint O, with the column OC perpendicular to the ground. If the A end of the horizontal board AB is on the ground and the angle OAC measures 28.0 degrees, what is th... | [
"mulberry_images/geoqa_plus/5692.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-195097 | [
{
"from": "user",
"value": "<image>Given that AB is 2.0 and BC is 3.0, and lines l_{1.0}, l_{2.0}, and l_{3.0} are parallel, what would be the length of DE if DF measures 4.0?\nChoices:\nA: \\frac{4}{3}\nB: \\frac{5}{4}\nC: \\frac{8}{5}\nD: 2"
},
{
"from": "assistant",
"value": "<think> Okay, le... | [
"mulberry_images/geoqa_plus/4683.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-195098 | [
{
"from": "user",
"value": "<image>The diagram shows triangle ABC with points D and E positioned on sides AC and BC, and DE parallel to AB. If the ratio of AD to DC is 1.0:2.0 and the area of triangle ABC is 18.0, what would be the area of triangle DEC?\nChoices:\nA: 8\nB: 9\nC: 12\nD: 15"
},
{
"fro... | [
"mulberry_images/geoqa_plus/7661.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-195099 | [
{
"from": "user",
"value": "<image>As depicted in the figure, circle O is shown with diameter AB forming a right angle with CD at the foot of the perpendicular, labeled E. Given that angle BOD is 48.0 degrees, what is the measure of angle BAC?\nChoices:\nA: 60°\nB: 48°\nC: 30°\nD: 24°"
},
{
"from": ... | [
"mulberry_images/geoqa_plus/211.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-195100 | [
{
"from": "user",
"value": "<image>If the city government plans to construct an overpass with a height of AB equal to 6.0, and the slope ratio is 3.0:4.0, what would be the length of the slope AC?\nChoices:\nA: 10\nB: 8\nC: 6\nD: 6√{3}"
},
{
"from": "assistant",
"value": "<think> Okay, let's see... | [
"mulberry_images/geoqa_plus/7879.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-195101 | [
{
"from": "user",
"value": "<image>In the given context, the angle CAB is identified as the circumferential angle of circle O, marked as 'x' degrees, where x = 50.0. What is the magnitude of the central angle angle BOC?\nChoices:\nA: 40°\nB: 50°\nC: 80°\nD: 100°"
},
{
"from": "assistant",
"value... | [
"mulberry_images/geoqa_plus/1724.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-195102 | [
{
"from": "user",
"value": "<image>Given the figure showing the rotation of square OABC by 40.0 degrees in the counterclockwise direction around point O, resulting in square ODEF, and the connection of points A and F, what is the degree measure of angle OFA?\nChoices:\nA: 15°\nB: 20°\nC: 25°\nD: 30°"
},
... | [
"mulberry_images/geoqa_plus/207.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-195103 | [
{
"from": "user",
"value": "<image>In the given diagram, circle O is illustrated with AB as its diameter and CD as a perpendicular chord. If the angle BOC measures 80 degrees, what is the measure of angle BAD? \nChoices:\nA: 10°\nB: 40°\nC: 45°\nD: 80°"
},
{
"from": "assistant",
"value": "<think... | [
"mulberry_images/geoqa_plus/2068.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-195104 | [
{
"from": "user",
"value": "<image>As shown in the figure, in triangle ABC, angle C = 90°, AC = 3, BC = 2. A square is constructed on the outside of the triangle with AB as one of its sides. The area of the square is ().\nChoices:\nA: 5\nB: 6\nC: 12\nD: 13"
},
{
"from": "assistant",
"value": "<t... | [
"mulberry_images/geoqa_plus/11428.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-195105 | [
{
"from": "user",
"value": "<image>How high is the flagpole AB if angle ACB is 30 degrees, CD measures 36.0, and angle ACD equals angle ACB with DA being perpendicular to AC at point A?\nChoices:\nA: 9m\nB: 18m\nC: 36m\nD: 72m"
},
{
"from": "assistant",
"value": "<think> Okay, let's see. There's... | [
"mulberry_images/geoqa_plus/5887.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-195106 | [
{
"from": "user",
"value": "<image>In the Cartesian coordinate system, point P is located at (2,4) and forms an angle α with the positive x-axis. By expressing the value of sinα as an expression involving x and y, determine sinα for point P.\nChoices:\nA: 0.5\nB: \\frac{√3}{2}\nC: \\frac{√5}{5}\nD: \\frac{2... | [
"mulberry_images/geoqa_plus/10621.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-195107 | [
{
"from": "user",
"value": "<image>Given that line l is parallel to line n, with line a intersecting l and n at points A, B, and C, and a new line b drawn crossing point B and intersecting lines l and n at points D and E, and AB = 2.0, BC = 1.0, and BD = 3.0, what is the value of BE?\nChoices:\nA: 4\nB: 2\n... | [
"mulberry_images/geoqa_plus/4688.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-195108 | [
{
"from": "user",
"value": "<image>If quadrilateral ABCD has AB parallel to CD and AD parallel to BC, with the angular bisectors AE and DF of angle BAD and angle ADC intersecting BC at points E and F, and EF measuring 2.0 and AB measuring 5.0, what is the length of AD?\nChoices:\nA: 7\nB: 6\nC: 8\nD: 9"
}... | [
"mulberry_images/geoqa_plus/5798.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-195109 | [
{
"from": "user",
"value": "<image>In the given figure, if the radius of the bottom surface of the cone is represented by 'r' units (r = 1.0), and the length of the generatrix is denoted by 'g' units (g = 3.0), what is the lateral area of the cone in terms of 'r' and 'g'?\nChoices:\nA: π\nB: 2π\nC: 3π\nD: 4... | [
"mulberry_images/geoqa_plus/2207.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-195110 | [
{
"from": "user",
"value": "<image>In triangle ABC, DE is parallel to BC. Given that AD measures 2.0 units and BD measures 3.0 units, find the value of the ratio DE:BC.\nChoices:\nA: \\frac{2}{3}\nB: \\frac{3}{2}\nC: \\frac{2}{5}\nD: \\frac{5}{2}"
},
{
"from": "assistant",
"value": "<think> Okay... | [
"mulberry_images/geoqa_plus/7954.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-195111 | [
{
"from": "user",
"value": "<image>As indicated in the figure, the square ABCD has a side length of 4.0 units. Point E is positioned on the side DC, and the length of DE is measured at 1.0 unit. The extended line segments BE and AD intersect at a point labeled F. What is the measurement of DF?\nChoices:\nA:... | [
"mulberry_images/geoqa_plus/7445.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-195112 | [
{
"from": "user",
"value": "<image>If the planned overpass by the city government has a height of AB equal to 6.0 and a slope ratio of 3.0:4.0, what will be the length of the slope AC?\nChoices:\nA: 10\nB: 8\nC: 6\nD: 6√{3}"
},
{
"from": "assistant",
"value": "<think> Okay, let's see. The proble... | [
"mulberry_images/geoqa_plus/7879.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-195113 | [
{
"from": "user",
"value": "<image>Given the figure depicting triangle ABC, where angle ABC measures 70.0 degrees and angle ACB measures 60.0 degrees, and the perpendicularity of line segment BE to line segment AC at point E, as well as the perpendicularity of line segment CF to line segment AB at point F, ... | [
"mulberry_images/geoqa_plus/757.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-195114 | [
{
"from": "user",
"value": "<image>In the provided image, Xiaoming can be seen utilizing a self-made right triangular cardboard DEF to evaluate the height of the tree AB. In order to achieve accurate results, Xiaoming positioned himself in such a way that the hypotenuse DF remained level, and the side DE an... | [
"mulberry_images/geoqa_plus/2306.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-195115 | [
{
"from": "user",
"value": "<image>In the figure provided, circle O has AB as its diameter. Point D and C lie on circle O. If we connect AD, BD, DC, AC, and angle BAD measures 25.0 degrees, what is the measurement of angle C?\nChoices:\nA: 75°\nB: 65°\nC: 60°\nD: 50°"
},
{
"from": "assistant",
"... | [
"mulberry_images/geoqa_plus/493.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-195116 | [
{
"from": "user",
"value": "<image>Within the provided figure, point D is located on the circumferential arc AC of isosceles triangle ABC, where the lengths of sides AB and AC are equal. Given that angle CAB equals 56.0 degrees, what is the measure of angle ADC?\nChoices:\nA: 116°\nB: 118°\nC: 122°\nD: 126°... | [
"mulberry_images/geoqa_plus/5546.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-195117 | [
{
"from": "user",
"value": "<image>As depicted in the figure, circle C has a radius of 2.0 units. Point O is located outside the circle, 3.5 units away from point C. Point P can move along the circle. On the line passing through O, there are two points A and B, where OA is equal to OB. The angle APB measure... | [
"mulberry_images/geoqa_plus/1708.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-195118 | [
{
"from": "user",
"value": "<image>Given the figure with the intersection of straight lines AB and CD at point O, and OC bisecting angle BOE, calculate the measure of angle AOD when the angle AOE measures 80.0 degrees.\nChoices:\nA: 80°\nB: 70°\nC: 60°\nD: 50°"
},
{
"from": "assistant",
"value":... | [
"mulberry_images/geoqa_plus/661.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-195119 | [
{
"from": "user",
"value": "<image>A sector with a radius of 6cm and a central angle of 120° is given. Determine the area of the sector and express it as a function of the radius 'r' and the central angle 'θ'.\nChoices:\nA: 6πcm2\nB: 9πcm2\nC: 12πcm2\nD: 18πcm2"
},
{
"from": "assistant",
"value"... | [
"mulberry_images/geoqa_plus/11672.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-195120 | [
{
"from": "user",
"value": "<image>In the provided figure, where AB and CD are parallel lines, if angle A is given as 50.0 degrees and angle C is given as 30.0 degrees, what is the measure of angle 1?\nChoices:\nA: 20°\nB: 30°\nC: 50°\nD: 80°"
},
{
"from": "assistant",
"value": "<think> Okay, le... | [
"mulberry_images/geoqa_plus/4928.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-195121 | [
{
"from": "user",
"value": "<image>Considering the figure provided, if angle AOB measures 50.0 degrees and angle OBC measures 40.0 degrees, what is the measure of angle OAC?\nChoices:\nA: 15°\nB: 25°\nC: 30°\nD: 40°"
},
{
"from": "assistant",
"value": "<think> Okay, let's see. The problem gives ... | [
"mulberry_images/geoqa_plus/1872.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-195122 | [
{
"from": "user",
"value": "<image>What is the degree measure of angle BIC in triangle ABC, where angle A is known to be 66.0 degrees and point I represents the incenter?\nChoices:\nA: 114°\nB: 122°\nC: 123°\nD: 132°"
},
{
"from": "assistant",
"value": "<think> Okay, let's see. The problem is as... | [
"mulberry_images/geoqa_plus/567.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-195123 | [
{
"from": "user",
"value": "<image>In the given figure, AB represents the diameter of circle O, while points C and D lie on the circumference of circle O. If angle BOC measures 116.0 degrees and AD is parallel to OC, determine the measure of angle AOD.\nChoices:\nA: 30°\nB: 64°\nC: 54°\nD: 52°"
},
{
... | [
"mulberry_images/geoqa_plus/8444.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-195124 | [
{
"from": "user",
"value": "<image>Refer to the provided diagram, where AB serves as the diameter of circle O, and points C and D lie on the circle. If the measure of arc AD is equal to the measure of arc CD, and angle CAB measures 40.0 degrees, what is the measure of angle CAD?\nChoices:\nA: 25°\nB: 50°\nC... | [
"mulberry_images/geoqa_plus/1890.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-195125 | [
{
"from": "user",
"value": "<image>When examining the parallelogram ABCD, assume points E and F lie on the extended lines of CD and BC, with AE parallel to BD and EF perpendicular to BF. Also, if angle ABC equals 60.0 degrees and EF measures 3.0 units, what is the length of AB?\nChoices:\nA: \\frac{2}{3}\nB... | [
"mulberry_images/geoqa_plus/5743.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-195126 | [
{
"from": "user",
"value": "<image>What is the area of the shaded part in the figure when three circles with radii of 2.0 are placed with a separation of two?\nChoices:\nA: π\nB: 2π\nC: 3π\nD: 4π"
},
{
"from": "assistant",
"value": "<think> Okay, so I need to find the area of the shaded part whe... | [
"mulberry_images/geoqa_plus/6712.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-195127 | [
{
"from": "user",
"value": "<image>What is the value of distance BC between the ladder and the corner of the wall if the angle ABC measures 60.0 degrees and the length of the ladder is 5.0, as depicted in the figure?\nChoices:\nA: 5\nB: 2.5\nC: 4\nD: 3"
},
{
"from": "assistant",
"value": "<think... | [
"mulberry_images/geoqa_plus/5888.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-195128 | [
{
"from": "user",
"value": "<image>In triangle ABC, where vertices D and E lie on the sides AB and AC respectively, if the ratios AD/BD and AE/EC are both equal to 1/2 and the length of DE is 3.0, what is the value of BC?\nChoices:\nA: 6\nB: 8\nC: 9\nD: 10"
},
{
"from": "assistant",
"value": "<t... | [
"mulberry_images/geoqa_plus/7270.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-195129 | [
{
"from": "user",
"value": "<image>Given the figure, point P is situated within angle AOB and serves as the symmetrical point with respect to OA and OB, labeled as P1.0 and P2.0 respectively. With P1.0P2.0 measuring 6.0, what is the perimeter of triangle PMN, where P1.0P2.0 intersects OA at M and OB at N?\n... | [
"mulberry_images/geoqa_plus/5671.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-195130 | [
{
"from": "user",
"value": "<image>In the provided diagram, triangle OAD and triangle OBC are congruent. If the measure of angle O is 70.0 degrees and the measure of angle C is 25.0 degrees, what is the measure of angle OAD?\nChoices:\nA: 95°\nB: 85°\nC: 75°\nD: 65°"
},
{
"from": "assistant",
"v... | [
"mulberry_images/geoqa_plus/70.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-195131 | [
{
"from": "user",
"value": "<image>Considering circle O with diameter AB and point C situated on circle O, along with radius OD being parallel to AC, if the angle BOD measures 130.0 degrees, what is the degree measurement of angle B?\nChoices:\nA: 30°\nB: 40°\nC: 50°\nD: 60°"
},
{
"from": "assistant... | [
"mulberry_images/geoqa_plus/1787.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-195132 | [
{
"from": "user",
"value": "<image>In the figure provided, if we take each vertex of the quadrilateral ABCD as the center and draw circles with a radius of 1.0, what is the total area covered by the shaded sectors?\nChoices:\nA: 2π\nB: π\nC: \\frac{2}{3}π\nD: \\frac{π}{2}"
},
{
"from": "assistant",
... | [
"mulberry_images/geoqa_plus/2004.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-195133 | [
{
"from": "user",
"value": "<image>In the provided figure, angle BOC is measured at 70.0 degrees. What would the degree measure of angle A be, considering that points A, B, and C are on circle O?\nChoices:\nA: 35°\nB: 45°\nC: 40°\nD: 70°"
},
{
"from": "assistant",
"value": "<think> Okay, so ther... | [
"mulberry_images/geoqa_plus/818.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-195134 | [
{
"from": "user",
"value": "<image>Triangle ABC is known to be similar to triangle DEB, with the length of BE being 3.0 and CE being 2.0. What is the result of the fraction EDAB?\nChoices:\nA: \\frac{3}{5}\nB: \\frac{5}{3}\nC: \\frac{2}{5}\nD: \\frac{5}{2}"
},
{
"from": "assistant",
"value": "<t... | [
"mulberry_images/geoqa_plus/4829.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-195135 | [
{
"from": "user",
"value": "<image>In parallelogram OABC, if the vertices A and C are located on the straight lines x = 1.0 and x = 4.0, and the origin O is at the intersection of the adjacent sides, what is the smallest length of the diagonal OB?\nChoices:\nA: 3\nB: 4\nC: 5\nD: 6"
},
{
"from": "ass... | [
"mulberry_images/geoqa_plus/5709.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-195136 | [
{
"from": "user",
"value": "<image>In the figure provided, it is indicated that BE is parallel to CF and CF is parallel to DG. Given that AB is to BC is to CD in the ratio of 2:1:3, and AE equals 4.0, what is the value of EG?\nChoices:\nA: 2\nB: 4\nC: 8\nD: 12"
},
{
"from": "assistant",
"value":... | [
"mulberry_images/geoqa_plus/4522.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-195137 | [
{
"from": "user",
"value": "<image>Given the layout where two points A and B are positioned at opposite ends of a pond, Xiao Cong intends to determine the distance between A and B using a rope that is too short. A classmate suggested marking a spot C on the ground, drawing lines from C to A and B, locating ... | [
"mulberry_images/geoqa_plus/168.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-195138 | [
{
"from": "user",
"value": "<image>Given the figure provided, where AB is the diameter of the semicircle and O is the center of the circle, C and D are located on the semicircle. If the measure of angle ACO is 20 degrees, then what is the degree measurement of angle D?\nChoices:\nA: 100°\nB: 110°\nC: 115°\n... | [
"mulberry_images/geoqa_plus/1785.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-195139 | [
{
"from": "user",
"value": "<image>In the diagram, let A, B, and C be points on the circumference of circle O. If the measure of angle C is 35.0 degrees, what is the measure of angle AOB? Represent the measure of angle AOB as 'x'.\nChoices:\nA: 35°\nB: 55°\nC: 65°\nD: 70°"
},
{
"from": "assistant",
... | [
"mulberry_images/geoqa_plus/8458.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-195140 | [
{
"from": "user",
"value": "<image>In the figure, triangle ABC is displayed, where angle ABC measures 45 degrees and side AC measures 8 units. If the height AD intersects with BE at point F, what is the length of BF?\nChoices:\nA: 4cm\nB: 6cm\nC: 8cm\nD: 9cm"
},
{
"from": "assistant",
"value": "... | [
"mulberry_images/geoqa_plus/45.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-195141 | [
{
"from": "user",
"value": "<image>Given the geometric illustration demonstrating triangle ABC, with points D, E, and Q situated on the edges AB, AC, and BC respectively, and DE being parallel to BC, it is worth noting that point P marks the intersection of AQ and DE. If the ratio DP/BQ is equal to 3/5, wha... | [
"mulberry_images/geoqa_plus/7374.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-195142 | [
{
"from": "user",
"value": "<image>Given that angle BOC measures 70.0 degrees and points A, B, and C lie on circle O, what can you determine about the degree measure of angle A?\nChoices:\nA: 35°\nB: 45°\nC: 40°\nD: 70°"
},
{
"from": "assistant",
"value": "<think> Okay, so there's this circle wi... | [
"mulberry_images/geoqa_plus/818.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-195143 | [
{
"from": "user",
"value": "<image>As shown in the diagram, in triangle ABC, AB = AC. Point P is a point inside triangle ABC, and angle PBC = angle PCA. If angle BPC = 115°, then the degree measure of angle A is ().\nChoices:\nA: 50°\nB: 55°\nC: 60°\nD: 65°"
},
{
"from": "assistant",
"value": "<... | [
"mulberry_images/geoqa_plus/10456.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-195144 | [
{
"from": "user",
"value": "<image>In the given figure, vertices A, B, and C are on circle O. If the measure of angle BOC is 72.0 degrees, what is the measure of angle BAC? Express the measure of angle BAC as 'x'.\nChoices:\nA: 36°\nB: 26°\nC: 72°\nD: 108°"
},
{
"from": "assistant",
"value": "<t... | [
"mulberry_images/geoqa_plus/8645.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-195145 | [
{
"from": "user",
"value": "<image>In the given scenario where a ladder leans against a wall, with the angle between the ladder and the ground being 60.0 degrees and the length of the ladder being 5.0, what is the distance BC between the ladder and the corner of the wall?\nChoices:\nA: 5\nB: 2.5\nC: 4\nD: 3... | [
"mulberry_images/geoqa_plus/5888.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-195146 | [
{
"from": "user",
"value": "<image>If the government of Huoqiu County intends to build an overpass with a height of 6.0, and the angle formed between the slope AC and the ground BC is angle ACB, where sin(angle ACB) is 3.0/5.0, what will be the length of the slope AC?\nChoices:\nA: 6√{3}m\nB: 10m\nC: 8m\nD:... | [
"mulberry_images/geoqa_plus/7855.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-195147 | [
{
"from": "user",
"value": "<image>As shown in the figure, in triangle ABC, points D and E are on AB and AC respectively, DE parallel BC. If AD = 4.0, DB = 2.0, then the value of frac DEBC is ()\nChoices:\nA: \\frac{1}{2}\nB: \\frac{2}{3}\nC: \\frac{3}{4}\nD: 2"
},
{
"from": "assistant",
"valu... | [
"mulberry_images/geoqa_plus/7779.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-195148 | [
{
"from": "user",
"value": "<image>In the given diagram, point P is located within angle AOB and serves as the symmetrical point with respect to OA and OB, marked as P1.0 and P2.0 respectively. Assuming P1.0P2.0 measures 6.0, what is the perimeter of triangle PMN, where P1.0P2.0 intersects OA at M and OB at... | [
"mulberry_images/geoqa_plus/5671.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-195149 | [
{
"from": "user",
"value": "<image>Given that equilateral triangle ABC has a side length of 3.0 units, point P is positioned on BC such that BP measures 1.0 unit, and angle APD measures 60.0 degrees, what is the length of CD if point D lies on AC?\nChoices:\nA: \\frac{4}{5}\nB: \\frac{3}{4}\nC: \\frac{2}{3}... | [
"mulberry_images/geoqa_plus/7404.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-195150 | [
{
"from": "user",
"value": "<image>What is the area of the shaded part in the figure where the sector AOB has a radius of 2.0, a central angle of 90.0 degrees, and AB is connected?\nChoices:\nA: π-2\nB: π-4\nC: 4π-2\nD: 4π-4"
},
{
"from": "assistant",
"value": "<think> Okay, let's see. The probl... | [
"mulberry_images/geoqa_plus/6500.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-195151 | [
{
"from": "user",
"value": "<image>Given that angle BOC measures 70.0 degrees in the provided figure, what is the degree measure of angle A if points A, B, and C are on circle O?\nChoices:\nA: 35°\nB: 45°\nC: 40°\nD: 70°"
},
{
"from": "assistant",
"value": "<think> Okay, so I have this geometry ... | [
"mulberry_images/geoqa_plus/818.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-195152 | [
{
"from": "user",
"value": "<image>In the given figure, triangle ABC is shown. If DE is parallel to BC and the lengths of AD and DB are 1.0 and 2.0 respectively, what is the ratio of DE to BC?\nChoices:\nA: \\frac{2}{3}\nB: \\frac{1}{4}\nC: \\frac{1}{3}\nD: \\frac{1}{2}"
},
{
"from": "assistant",
... | [
"mulberry_images/geoqa_plus/7449.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-195153 | [
{
"from": "user",
"value": "<image>If angle 1 is measured as 48.0 degrees in the given figure, and a right triangle plate is positioned with its right-angled vertex on one side of the ruler, what is the measure of angle 2?\nChoices:\nA: 48°\nB: 42°\nC: 40°\nD: 45°"
},
{
"from": "assistant",
"val... | [
"mulberry_images/geoqa_plus/601.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-195154 | [
{
"from": "user",
"value": "<image>In the diagram, BC represents the diameter of circle O. If angle ABC measures 25.0 degrees, what is the measure of angle ADB? Express the measure of angle ADB as ϕ.\nChoices:\nA: 25°\nB: 65°\nC: 75°\nD: 无法确定"
},
{
"from": "assistant",
"value": "<think> Alright,... | [
"mulberry_images/geoqa_plus/8716.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-195155 | [
{
"from": "user",
"value": "<image>On the given circle, if angle 1 is 68.0 degrees and angle A is 40.0 degrees, what is the degree measure of angle D? \nChoices:\nA: 68°\nB: 40°\nC: 28°\nD: 22°"
},
{
"from": "assistant",
"value": "<think> Okay, let's try to figure out the measure of angle D. So,... | [
"mulberry_images/geoqa_plus/5471.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-195156 | [
{
"from": "user",
"value": "<image>In the given figure, triangle ABC is circumscribed by a circle O. If angle A measures 30.0 degrees and BC measures 2.0 units, what is the radius of circle O? Represent the radius as 'r'.\nChoices:\nA: 1\nB: 2\nC: √{3}\nD: 4"
},
{
"from": "assistant",
"value": "... | [
"mulberry_images/geoqa_plus/9861.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-195157 | [
{
"from": "user",
"value": "<image>What is the diameter of circle O when the length of chord AB is 8.0 and the distance from center O to AB is 3.0?\nChoices:\nA: 5cm\nB: 10cm\nC: 6cm\nD: 14cm"
},
{
"from": "assistant",
"value": "<think> Okay, let's see. I need to find the diameter of the circle ... | [
"mulberry_images/geoqa_plus/5206.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-195158 | [
{
"from": "user",
"value": "<image>In the plane rectangular coordinate system, point A is given as (4.0, 2.0). Drawing a perpendicular line from A to the x-axis at point B forms triangle AOB. If triangle AOB is dilated by a scale factor of frac{1.0}{2.0} with the origin O as the center of dilation and reduc... | [
"mulberry_images/geoqa_plus/5589.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-195159 | [
{
"from": "user",
"value": "<image>What is the measure of angle BAC in triangle ABC if point I serves as the incenter and angle BIC equals 130.0 degrees?\nChoices:\nA: 60°\nB: 65°\nC: 70°\nD: 80°"
},
{
"from": "assistant",
"value": "<think> Okay, so the problem is about triangle ABC with incente... | [
"mulberry_images/geoqa_plus/5558.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-195160 | [
{
"from": "user",
"value": "<image>The picture illustrates an ancient masher located in a rural area. The height of the support column AB is 0.3, the length of the pedal DE is 1.6, and the distance from the support point A to the foot D is 0.6. When the ground is pressed down by stepping on it, how much doe... | [
"mulberry_images/geoqa_plus/2360.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-195161 | [
{
"from": "user",
"value": "<image>What is the value of sinB in triangle ABC if AB = AC = 10.0 and BC = 12.0?\nChoices:\nA: \\frac{4}{5}\nB: \\frac{3}{5}\nC: \\frac{4}{3}\nD: \\frac{3}{4}"
},
{
"from": "assistant",
"value": "<think> Okay, let's see. I need to find sin B in triangle ABC where AB ... | [
"mulberry_images/geoqa_plus/5539.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-195162 | [
{
"from": "user",
"value": "<image>As shown in the figure, vertices A, B, C are on circle O, angle A = 64.0, then the degree of angle BOC is ()\nChoices:\nA: 26°\nB: 116°\nC: 128°\nD: 154°"
},
{
"from": "assistant",
"value": "<think> Okay, let me try to figure this out. So, there's a circle with... | [
"mulberry_images/geoqa_plus/8584.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-195163 | [
{
"from": "user",
"value": "<image>Considering the figure where AB is parallel to CD and the ratio of AO to OD is 2.0 to 3.0, what is the ratio of the areas of triangle AOB to triangle DOC?\nChoices:\nA: \\frac{4}{9}\nB: \\frac{3}{2}\nC: \\frac{2}{5}\nD: \\frac{2}{3}"
},
{
"from": "assistant",
"... | [
"mulberry_images/geoqa_plus/7489.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-195164 | [
{
"from": "user",
"value": "<image>In the accompanying figure showing triangle ABC, the measure of angle A is set at 90 degrees. Point D is situated on the side AC, and DE is parallel to BC. If angle 1 measures 155 degrees, what is the degree measurement of angle B?\nChoices:\nA: 45°\nB: 55°\nC: 65°\nD: 75°... | [
"mulberry_images/geoqa_plus/183.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-195165 | [
{
"from": "user",
"value": "<image>In the figure, triangles ACD and ABD are symmetric with respect to the line containing the segment AD, and the points B, D, and C are collinear. If AC is 3.0 and BD is 2.0, what is the perimeter of triangle ABC?\nChoices:\nA: 5\nB: 10\nC: 6\nD: 12"
},
{
"from": "as... | [
"mulberry_images/geoqa_plus/5648.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-195166 | [
{
"from": "user",
"value": "<image>In the provided diagram, circle O is depicted, with point M as the point of intersection for the longest chord measuring 12.0 units and the shortest chord measuring 8.0 units. What is the length of OM?\nChoices:\nA: 6cm\nB: 2√{5}cm\nC: 4√{5}cm\nD: 9cm"
},
{
"from":... | [
"mulberry_images/geoqa_plus/5103.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-195167 | [
{
"from": "user",
"value": "<image>As depicted in the figure, in quadrilateral ABCD, with P being the midpoint of diagonal BD, E being the midpoint of AB, F being the midpoint of CD, and AD being equal to BC, if angle PEF equals 18.0 degrees, what is the measure of angle PFE?\nChoices:\nA: 9°\nB: 18°\nC: 27... | [
"mulberry_images/geoqa_plus/5968.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-195168 | [
{
"from": "user",
"value": "<image>Let us consider circle A, where points B, C, and D lie on its circumference. The measure of angle CBD is two times the measure of angle BDC. Given that the measure of angle BAC is 44.0 degrees, what is the measure of angle CAD?\nChoices:\nA: 68°\nB: 88°\nC: 90°\nD: 112°"
... | [
"mulberry_images/geoqa_plus/1853.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-195169 | [
{
"from": "user",
"value": "<image>Given an equilateral triangle ABC with side length 6.0, point P on BC, PC measuring 4.0, and point D on AC with angle APD measuring 60.0, what is the length of CD? Represent the length as 'x'.\nChoices:\nA: \\frac{3}{4}\nB: \\frac{4}{9}\nC: \\frac{4}{3}\nD: \\frac{1}{9}"
... | [
"mulberry_images/geoqa_plus/8385.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-195170 | [
{
"from": "user",
"value": "<image>What is the measure of angle P if AB is the diameter of circle O, PC is a tangent to the circle, and angle A measures 30 degrees as shown in the figure?\nChoices:\nA: 50°\nB: 30°\nC: 20°\nD: 45°"
},
{
"from": "assistant",
"value": "<think> Okay, so I need to fi... | [
"mulberry_images/geoqa_plus/4446.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-195171 | [
{
"from": "user",
"value": "<image>In a cone, the radius of the base is represented by 'r' units (r = 3.0), and the length of the generatrix is symbolized by 'g' units (g = 4.0). Determine the lateral area 'L' units of the cone.\nChoices:\nA: 24π\nB: 12π\nC: 6π\nD: 12"
},
{
"from": "assistant",
... | [
"mulberry_images/geoqa_plus/2222.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-195172 | [
{
"from": "user",
"value": "<image>Given a regular hexagon ABCDEF inscribed in circle O with a radius of 6.0, what is the area of the shaded part in the diagram?\nChoices:\nA: 12π\nB: 6π\nC: 9π\nD: 18π"
},
{
"from": "assistant",
"value": "<think> Okay, let's see. The problem is about a regular h... | [
"mulberry_images/geoqa_plus/595.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-195173 | [
{
"from": "user",
"value": "<image>In the provided diagram, two right triangle plates with angles measuring 30.0 and 45.0 degrees respectively are combined to form a larger figure. With angle C measuring 90.0 degrees, angle B measuring 45.0 degrees, and angle E measuring 30.0 degrees, what is the degree mea... | [
"mulberry_images/geoqa_plus/54.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-195174 | [
{
"from": "user",
"value": "<image>As shown in the figure, in Rttriangle ABC, angle C = 90.0, AB = 5.0, AC = 2.0, then the value of cosA is ()\nChoices:\nA: \\frac{√{21}}{5}\nB: \\frac{2}{5}\nC: \\frac{√{21}}{2}\nD: \\frac{5}{2}"
},
{
"from": "assistant",
"value": "<think> Okay, let's see. The p... | [
"mulberry_images/geoqa_plus/7077.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-195175 | [
{
"from": "user",
"value": "<image>In the given figure, with AB being parallel to CD and the lengths of AO, BO, and CO being 2.0, 3.0, and 6.0, what is the magnitude of DO?\nChoices:\nA: 3\nB: 4\nC: 5\nD: 6"
},
{
"from": "assistant",
"value": "<think> Okay, let me try to figure this out. So, the... | [
"mulberry_images/geoqa_plus/4703.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-195176 | [
{
"from": "user",
"value": "<image>Illustrated in the figure, triangle OAD and triangle OBC are congruent. If the measure of angle O is 70.0 degrees and the measure of angle C is 25.0 degrees, what is the measure of angle OAD?\nChoices:\nA: 95°\nB: 85°\nC: 75°\nD: 65°"
},
{
"from": "assistant",
... | [
"mulberry_images/geoqa_plus/70.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-195177 | [
{
"from": "user",
"value": "<image>In the figure provided, point O is the intersection of lines AB and CD. Line EF is perpendicular to AB at point O. What is the measure of angle BOD when angle COE is 50.0 degrees? \nChoices:\nA: 40°\nB: 45°\nC: 55°\nD: 65°"
},
{
"from": "assistant",
"value": "<... | [
"mulberry_images/geoqa_plus/574.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-195178 | [
{
"from": "user",
"value": "<image>Given that AB and CD are parallel in the provided figure and the fraction AO/OD is expressed as 2.0/3.0, what is the ratio of the areas of triangle AOB to triangle DOC?\nChoices:\nA: \\frac{4}{9}\nB: \\frac{3}{2}\nC: \\frac{2}{5}\nD: \\frac{2}{3}"
},
{
"from": "ass... | [
"mulberry_images/geoqa_plus/7489.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-195179 | [
{
"from": "user",
"value": "<image>In the figure illustrating a river embankment's cross section, the slope AB has a slope ratio of 1.0:2.0, while the height of the embankment BC is 5.0. What is the length of slope AB?\nChoices:\nA: 10m\nB: 10√{5}m\nC: 15m\nD: 5√{5}m"
},
{
"from": "assistant",
"... | [
"mulberry_images/geoqa_plus/7323.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-195180 | [
{
"from": "user",
"value": "<image>In the given Cartesian coordinate system, the terminal side of angle α intersects the point P with coordinates (2.0, 3.0), while the initial side lies along the positive semiaxis of the x-axis. What is the value of the tangent of angle α?\nChoices:\nA: \\frac{2}{3}\nB: \\f... | [
"mulberry_images/geoqa_plus/7109.png"
] | vision_r1_mulberry_sft_full |
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