id stringlengths 29 36 | conversations listlengths 1 48 | images listlengths 1 1 | source_dataset stringclasses 2
values |
|---|---|---|---|
vision_r1_mulberry_sft_full-194781 | [
{
"from": "user",
"value": "<image>In triangle ABC, DE is parallel to BC and AD to DB equals 1:3. What is the resulting ratio of DE to BC?\nChoices:\nA: \\frac{1}{2}\nB: \\frac{1}{3}\nC: \\frac{1}{4}\nD: \\frac{1}{5}"
},
{
"from": "assistant",
"value": "<think> Okay, let's tackle this problem. S... | [
"mulberry_images/geoqa_plus/4752.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194782 | [
{
"from": "user",
"value": "<image>Given the figure, where AB represents a chord of circle O and OC is perpendicular to AB at point C, with AB measuring 16.0 and OC measuring 6.0, what is the radius of circle O?\nChoices:\nA: 3cm\nB: 5cm\nC: 6cm\nD: 10cm"
},
{
"from": "assistant",
"value": "<thi... | [
"mulberry_images/geoqa_plus/5131.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194783 | [
{
"from": "user",
"value": "<image>When a sector-shaped piece of paper with a radius of 10.0 and a central angle of 144.0 is used to create a cone, what will be the measurement of the base radius?\nChoices:\nA: 3\nB: 4\nC: 5\nD: 6"
},
{
"from": "assistant",
"value": "<think> Okay, let's see. The... | [
"mulberry_images/geoqa_plus/2219.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194784 | [
{
"from": "user",
"value": "<image>In the diagram, circle O is depicted, with chord AB measuring 18.0 units. Additionally, M is identified as the midpoint of AB, and OM measures 12.0 units. What is the radius of circle O?\nChoices:\nA: 8\nB: 2\nC: 10\nD: 15"
},
{
"from": "assistant",
"value": "<... | [
"mulberry_images/geoqa_plus/5122.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194785 | [
{
"from": "user",
"value": "<image>When points A, B, and C lie on circle O and angle CAB is 70 degrees, what is the measure of angle COB?\nChoices:\nA: 70°\nB: 80°\nC: 120°\nD: 140°"
},
{
"from": "assistant",
"value": "<think> Okay, so I need to find the measure of angle COB given that angle CAB... | [
"mulberry_images/geoqa_plus/2278.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194786 | [
{
"from": "user",
"value": "<image>Provided in the figure is chord AE parallel to diameter CD, and both are even. If angle AOC is 40.0 degrees, what is the degree measure of the central angle of arc DE?\nChoices:\nA: 40°\nB: 50°\nC: 60°\nD: 30°"
},
{
"from": "assistant",
"value": "<think> Okay, ... | [
"mulberry_images/geoqa_plus/1697.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194787 | [
{
"from": "user",
"value": "<image>Consider the figure where the angle between the height PC of the cone and the generatrix PB measures 30.0 degrees. What will be the degree measure of the central angle of the expanded figure of the lateral surface?\nChoices:\nA: 90°\nB: 150°\nC: 180°\nD: 210°"
},
{
... | [
"mulberry_images/geoqa_plus/2030.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194788 | [
{
"from": "user",
"value": "<image>If AB is the diameter of circle O, CD is a chord, and AB is perpendicular to CD at E, with AB measuring 10.0 and OE measuring 3.0, what is the length of the chord CD?\nChoices:\nA: 4\nB: 8\nC: √{34}\nD: 2√{34}"
},
{
"from": "assistant",
"value": "<think> Okay, ... | [
"mulberry_images/geoqa_plus/5182.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194789 | [
{
"from": "user",
"value": "<image>If triangle ABC is shown with DE parallel to BC, intersecting AB at point D and AC at point E, and with AE measuring 4.0 and EC measuring 2.0, what is the value of BD:AB?\nChoices:\nA: 2\nB: \\frac{1}{2}\nC: \\frac{1}{3}\nD: \\frac{2}{3}"
},
{
"from": "assistant",
... | [
"mulberry_images/geoqa_plus/4726.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194790 | [
{
"from": "user",
"value": "<image>When points A, B, and C are positioned on circle O, and angle ABC is 40 degrees, what is the degree measure of angle AOC?\nChoices:\nA: 40°\nB: 50°\nC: 60°\nD: 80°"
},
{
"from": "assistant",
"value": "<think> Okay, so we have a circle with center O, and points ... | [
"mulberry_images/geoqa_plus/1881.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194791 | [
{
"from": "user",
"value": "<image>If a cone is formed by using a sector with a radius of 6.0 and a central angle of 120.0 degrees, what is the lateral area of the cone?\nChoices:\nA: 6\nB: 12\nC: 6π\nD: 12π"
},
{
"from": "assistant",
"value": "<think> Okay, let me try to figure out this problem... | [
"mulberry_images/geoqa_plus/2126.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194792 | [
{
"from": "user",
"value": "<image>As depicted in the figure, circle O has a radius of 5.0 and chord AB. If the distance from the center of the circle to chord AB is 3.0, determine the length of chord AB.\nChoices:\nA: 4cm\nB: 6cm\nC: 8cm\nD: 10cm"
},
{
"from": "assistant",
"value": "<think> Oka... | [
"mulberry_images/geoqa_plus/5130.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194793 | [
{
"from": "user",
"value": "<image>If a cone is formed by utilizing a sector with a radius of 3.0 and a central angle of 120.0 for its lateral surface, what will be the radius of its bottom?\nChoices:\nA: 2πcm\nB: 1.5cm\nC: πcm\nD: 1cm"
},
{
"from": "assistant",
"value": "<think> Okay, so I need... | [
"mulberry_images/geoqa_plus/2159.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194794 | [
{
"from": "user",
"value": "<image>In the diagram provided, with ABCD as the quadrilateral and the diagonals intersecting at point O, where AD is not equal to CD, and a perpendicular line from point O intersects AC at point M, if the perimeter of triangle CDM measures 40cm, what is the perimeter of parallel... | [
"mulberry_images/geoqa_plus/12464.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194795 | [
{
"from": "user",
"value": "<image>In the provided figure, where points A, B, and C lie on circle O, if angle BOC measures 50.0 degrees, what is the value of angle A?\nChoices:\nA: 25°\nB: 20°\nC: 80°\nD: 100°"
},
{
"from": "assistant",
"value": "<think> Okay, so there's a circle with center O. ... | [
"mulberry_images/geoqa_plus/1913.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194796 | [
{
"from": "user",
"value": "<image>In the provided figure, a conical chimney cap made of iron sheet has a bottom diameter of 80.0 and a height of 30.0. What is the minimum area of iron sheet required, excluding processing residual materials?\nChoices:\nA: 4000π(cm^{2})\nB: 2400π(cm^{2})\nC: 2000π(cm^{2})\nD... | [
"mulberry_images/geoqa_plus/2282.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194797 | [
{
"from": "user",
"value": "<image>As depicted in the figure, if AD is the diameter of circle O with a length of 8 cm, and angle DAC equals angle ABC, what is the dimension of AC?\nChoices:\nA: 4√{2}cm\nB: 2√{2}cm\nC: 4cm\nD: 3√{3}cm"
},
{
"from": "assistant",
"value": "<think> Okay, let me try ... | [
"mulberry_images/geoqa_plus/13109.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194798 | [
{
"from": "user",
"value": "<image>In the provided figure, if AB is parallel to CD and angle CEF measures 110 degrees, what is the degree measure of angle A?\nChoices:\nA: 90°\nB: 80°\nC: 70°\nD: 60°"
},
{
"from": "assistant",
"value": "<think> Okay, let's try to figure out the measure of angle ... | [
"mulberry_images/geoqa_plus/1502.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194799 | [
{
"from": "user",
"value": "<image>At a distance of around 30.0 meters from a telephone pole, a person uses a small ruler divided into centimeters to estimate the height of the pole. By extending their arm and standing the ruler upright, they observe that 12.0 divisions (12.0 centimeters) cover the wire Rod... | [
"mulberry_images/geoqa_plus/2461.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194800 | [
{
"from": "user",
"value": "<image>As shown in the figure, AD is the angle bisector of triangle ABC. DF is perpendicular to AB, with foot F. DE = DG. The areas of triangle ADG and triangle AED are 29 and 16 respectively. The area of triangle EDF is ()\nChoices:\nA: 13\nB: 6.5\nC: 11\nD: 5.5"
},
{
"f... | [
"mulberry_images/geoqa_plus/11420.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194801 | [
{
"from": "user",
"value": "<image>Consider the figure in which a large parasol is represented. When the surface of the umbrella is stretched, it can be approximately viewed as a conical shape. With a generatrix length of 2.5 and a height of 1.5, what is the area of the fabric required to construct this par... | [
"mulberry_images/geoqa_plus/2100.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194802 | [
{
"from": "user",
"value": "<image>When a circle is rotated along the line BC in right triangle ABC, where the hypotenuse AB measures 5.0 units and leg AC measures 3.0 units, what is the resulting lateral area of the cone?\nChoices:\nA: 8π\nB: 12π\nC: 15π\nD: 20π"
},
{
"from": "assistant",
"valu... | [
"mulberry_images/geoqa_plus/2277.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194803 | [
{
"from": "user",
"value": "<image>Considering the provided figure, where AB represents the chord of circle O and OC is a line perpendicular to AB at point C, with AB measuring 16.0 and OC measuring 6.0, what is the radius of circle O?\nChoices:\nA: 3cm\nB: 5cm\nC: 6cm\nD: 10cm"
},
{
"from": "assist... | [
"mulberry_images/geoqa_plus/5131.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194804 | [
{
"from": "user",
"value": "<image>Utilizing a sector with a radius of 30.0 and a central angle of 120.0 to form the lateral surface of a cone, what radius should be chosen for the bottom of the cone?\nChoices:\nA: 10cm\nB: 20cm\nC: 10πcm\nD: 20πcm"
},
{
"from": "assistant",
"value": "<think> Ok... | [
"mulberry_images/geoqa_plus/2018.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194805 | [
{
"from": "user",
"value": "<image>As depicted in the figure, a conical chimney cap made of iron sheet has a height of 30.0 and a bottom diameter of 80.0. What is the minimum area of iron sheet required, excluding processing residual materials?\nChoices:\nA: 4000π(cm^{2})\nB: 2400π(cm^{2})\nC: 2000π(cm^{2})... | [
"mulberry_images/geoqa_plus/2282.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194806 | [
{
"from": "user",
"value": "<image>Point D is located inside triangle ABC as shown in the diagram, where BD is perpendicular to CD. The midpoints of sides AB, BD, CD, and AC are labeled as E, F, G, and H respectively. If the lengths of AD, BD, and CD are 10, 8, and 6 respectively, what is the perimeter of q... | [
"mulberry_images/geoqa_plus/12981.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194807 | [
{
"from": "user",
"value": "<image>As depicted in the figure, triangle ABC is inscribed within circle O, where AD is the diameter of the circle. Given that angle ABC is 30 degrees, what is the degree measure of angle CAD?\nChoices:\nA: 45°\nB: 50°\nC: 55°\nD: 60°"
},
{
"from": "assistant",
"valu... | [
"mulberry_images/geoqa_plus/1654.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194808 | [
{
"from": "user",
"value": "<image>If a sector with a radius of 9.0 and a central angle of 120.0 is rolled into a cone (without overlap) as depicted in the figure, what will be the radius of the bottom circle of the cone?\nChoices:\nA: 1\nB: 2\nC: 3\nD: π"
},
{
"from": "assistant",
"value": "<th... | [
"mulberry_images/geoqa_plus/2122.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194809 | [
{
"from": "user",
"value": "<image>In the scenario presented, there are two points A and B positioned at the opposite ends of a pond, and Xiaoming endeavors to measure the distance between them. To achieve this, he introduces points C, D, and E, with specific relationships between their positions and distan... | [
"mulberry_images/geoqa_plus/2467.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194810 | [
{
"from": "user",
"value": "<image>If triangle ABC is congruent to triangle ADE and AB, BC, and AC measure 5.0, 7.0, and 6.0 in the figure, what is the length of DE?\nChoices:\nA: 6cm\nB: 5cm\nC: 7cm\nD: 无法确定"
},
{
"from": "assistant",
"value": "<think> Okay, so we have two congruent triangles, ... | [
"mulberry_images/geoqa_plus/5283.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194811 | [
{
"from": "user",
"value": "<image>If the bottom surface of a cone-shaped paper cup has a radius of 5.0 and the generatrix measures 15.0, what is the lateral area of the paper cup when represented as an expanded figure?\nChoices:\nA: 75πcm^{2}\nB: 150πcm^{2}\nC: \\frac{75π}{2}cm^{2}\nD: \\frac{375π}{2}cm^{2... | [
"mulberry_images/geoqa_plus/2054.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194812 | [
{
"from": "user",
"value": "<image>Given that AB is the diameter of circle O, and CD is a chord perpendicular to AB at E, where AB measures 10.0 and OE measures 3.0, what is the length of the chord CD?\nChoices:\nA: 4\nB: 8\nC: √{34}\nD: 2√{34}"
},
{
"from": "assistant",
"value": "<think> Okay, ... | [
"mulberry_images/geoqa_plus/5182.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194813 | [
{
"from": "user",
"value": "<image>What is the length of EF in the right triangle ABC, where angle ACB equals 90°, angle A equals 30°, D, E, and F are the midpoints of AB, AC, and AD respectively, and BC has a length of 2 units?\nChoices:\nA: 0.5\nB: 1\nC: 1.5\nD: √{3}"
},
{
"from": "assistant",
... | [
"mulberry_images/geoqa_plus/13039.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194814 | [
{
"from": "user",
"value": "<image>The radius of the bottom circle of the cone measures 3.0. What is the length of the arc of the sector of the expanded figure of the cone lateral surface?\nChoices:\nA: 2π\nB: 4π\nC: 6π\nD: 9π"
},
{
"from": "assistant",
"value": "<think> Okay, let's see. The pro... | [
"mulberry_images/geoqa_plus/2236.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194815 | [
{
"from": "user",
"value": "<image>In the provided figure, with points A, B, and C located on circle O and the degree of arc ACB measuring 300 degrees, what is the measure of angle C?\nChoices:\nA: 30°\nB: 40°\nC: 50°\nD: 60°"
},
{
"from": "assistant",
"value": "<think> Alright, let me try to fi... | [
"mulberry_images/geoqa_plus/1745.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194816 | [
{
"from": "user",
"value": "<image>If points A, B, and C are all on circle O as shown in the figure and the measure of angle ACB is 112.0 degrees, what is the degree measure of angle α? \nChoices:\nA: 68°\nB: 112°\nC: 136°\nD: 134°"
},
{
"from": "assistant",
"value": "<think> Okay, let's see. Th... | [
"mulberry_images/geoqa_plus/1755.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194817 | [
{
"from": "user",
"value": "<image>Consider the figure shown, where vertices A, B, and C are situated on the boundary of circle O. Connecting the points OA, OC, and OD, we find that OD is perpendicular to AB at point D. Given that angle CAB is equal to 50 degrees and angle CAB is bisected by line AO, what i... | [
"mulberry_images/geoqa_plus/1463.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194818 | [
{
"from": "user",
"value": "<image>Consider the figure shown, where a student with a height of 1.6 meters seeks to measure the height of a flagpole at their school. The student positions themselves at point C, and upon noticing that their head's shadow lines up with the shadow of the flagpole at point A, th... | [
"mulberry_images/geoqa_plus/2315.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194819 | [
{
"from": "user",
"value": "<image>As shown in the figure representing circle O, the diameter AB is perpendicular to chord CD, and point P marks the foot of the vertical. What is the radius of the circle if CD is 8.0 units and OP measures 3.0 units?\nChoices:\nA: 10\nB: 8\nC: 5\nD: 3"
},
{
"from": "... | [
"mulberry_images/geoqa_plus/5093.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194820 | [
{
"from": "user",
"value": "<image>In the given diagram, the bottom radius of the cone is OB = 6.0 and the height is OC = 8.0. Determine the lateral area of this cone.\nChoices:\nA: 30cm^{2}\nB: 30πcm^{2}\nC: 60πcm^{2}\nD: 120cm^{2}"
},
{
"from": "assistant",
"value": "<think> Okay, let's see. T... | [
"mulberry_images/geoqa_plus/2006.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194821 | [
{
"from": "user",
"value": "<image>Given that triangle ABC is shown in the figure with angle ABC equal to 90 degrees and angle A equal to 50 degrees, what is the degree measure of angle C?\nChoices:\nA: 50°\nB: 40°\nC: 30°\nD: 45°"
},
{
"from": "assistant",
"value": "<think> Okay, so there's thi... | [
"mulberry_images/geoqa_plus/1925.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194822 | [
{
"from": "user",
"value": "<image>In the given figure, if right triangle ABC is rotated around the line AC, creating a cone, what will be the surface area of the cone? The measurements of right triangle ABC are as follows: angle BAC measures 90 degrees, AB measures 2.0 units, and BC measures 5.0 units.\nCh... | [
"mulberry_images/geoqa_plus/2129.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194823 | [
{
"from": "user",
"value": "<image>If angle AOB is the central angle of circle O and measures 50.0 degrees, what is the degree measure of the circumference angle ACB shown in the figure?\nChoices:\nA: 50°\nB: 25°\nC: 100°\nD: 30°"
},
{
"from": "assistant",
"value": "<think> Okay, so I need to fi... | [
"mulberry_images/geoqa_plus/1850.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194824 | [
{
"from": "user",
"value": "<image>In the given figure, a cylinder is depicted with a height of 8.0 and a radius of the bottom surface measuring 3.0. If the cylinder is cut vertically along the diameter of the upper base using a plane, what is the area of the resulting section?\nChoices:\nA: 24\nB: 48\nC: 3... | [
"mulberry_images/geoqa_plus/2253.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194825 | [
{
"from": "user",
"value": "<image>In the provided figure, point P is situated outside circle O, where tangent lines PA and PB intersect circle O at points A and B, respectively. Given that angle P equals 50.0 degrees, what is the measure of angle AOB?\nChoices:\nA: 150°\nB: 130°\nC: 155°\nD: 135°"
},
{... | [
"mulberry_images/geoqa_plus/166.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194826 | [
{
"from": "user",
"value": "<image>When a triangular plank with legs measuring 6.0 and 8.0 is rotated around the side measured at 6.0, what is the total area swept by the hypotenuse during this rotation?\nChoices:\nA: 48πcm^{2}\nB: 60πcm^{2}\nC: 80πcm^{2}\nD: 90πcm^{2}"
},
{
"from": "assistant",
... | [
"mulberry_images/geoqa_plus/2056.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194827 | [
{
"from": "user",
"value": "<image>In the given figure showing triangle ABC, it is known that AD is the angular bisector of the triangle. DE is parallel to AB and intersects AC at point E. If AE/EC = 3/5, what can be said about the ratio of AC to AB?\nChoices:\nA: \\frac{3}{5}\nB: \\frac{5}{3}\nC: \\frac{8}... | [
"mulberry_images/geoqa_plus/4890.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194828 | [
{
"from": "user",
"value": "<image>What is the lateral area of the cone that is created by using a sector with a radius of 6.0 and a central angle of 120.0 degrees?\nChoices:\nA: 6\nB: 12\nC: 6π\nD: 12π"
},
{
"from": "assistant",
"value": "<think> Okay, let's see. The problem is about finding th... | [
"mulberry_images/geoqa_plus/2126.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194829 | [
{
"from": "user",
"value": "<image>Given that the generatrix of the cone is 10.0 and the diameter of the bottom circle is 12.0, what is the lateral surface area of the cone?\nChoices:\nA: 24π\nB: 30π\nC: 48π\nD: 60π"
},
{
"from": "assistant",
"value": "<think> Okay, let's see. The problem is ask... | [
"mulberry_images/geoqa_plus/2149.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194830 | [
{
"from": "user",
"value": "<image>In the given figure, if triangle ACD is similar to triangle BCA and CD has a length of 4.0 while AC has a length of 6.0, what is the measure of BC?\nChoices:\nA: 9\nB: 10\nC: 11\nD: 12"
},
{
"from": "assistant",
"value": "<think> Okay, so there are two similar ... | [
"mulberry_images/geoqa_plus/4810.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194831 | [
{
"from": "user",
"value": "<image>In circle O with a radius of 6.0, chord AB is perpendicular to the midpoint D of radius OC. How long is the chord AB?\nChoices:\nA: 4\nB: 5\nC: 3√{3}\nD: 6√{3}"
},
{
"from": "assistant",
"value": "<think> Okay, let's see. The problem is about a circle with cent... | [
"mulberry_images/geoqa_plus/5126.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194832 | [
{
"from": "user",
"value": "<image>Given that points A, B, and C are located on circle O and angle OAB is 65.0 degrees, what is the degree measure of angle ACB?\nChoices:\nA: 50°\nB: 32.5°\nC: 25°\nD: 20°"
},
{
"from": "assistant",
"value": "<think> Okay, let's see. The problem is about a circle... | [
"mulberry_images/geoqa_plus/1792.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194833 | [
{
"from": "user",
"value": "<image>Angle AOB, which is the central angle of circle O, measures 50.0 degrees. How many degrees does the circumference angle ACB measure?\nChoices:\nA: 50°\nB: 25°\nC: 100°\nD: 30°"
},
{
"from": "assistant",
"value": "<think> Okay, so I need to find the measure of a... | [
"mulberry_images/geoqa_plus/1850.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194834 | [
{
"from": "user",
"value": "<image>What is the lateral surface area of the cone if the generatrix measures 10.0 and the diameter of the bottom circle is 12.0, as shown in the figure?\nChoices:\nA: 24π\nB: 30π\nC: 48π\nD: 60π"
},
{
"from": "assistant",
"value": "<think> Okay, let's see. The que... | [
"mulberry_images/geoqa_plus/2149.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194835 | [
{
"from": "user",
"value": "<image>In order for Xiaohong to make a conical birthday hat with a bottom radius of 9.0 cm and a height of 12.0 cm using sector-shaped thin cardboard, what should be the measure of the central angle of the cardboard?\nChoices:\nA: 150°\nB: 180°\nC: 216°\nD: 270°"
},
{
"fr... | [
"mulberry_images/geoqa_plus/2194.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194836 | [
{
"from": "user",
"value": "<image>In the figure given, AB is the chord of circle O and OC is a perpendicular line to AB at point C. If AB measures 16.0 and OC measures 6.0, what is the radius of circle O?\nChoices:\nA: 3cm\nB: 5cm\nC: 6cm\nD: 10cm"
},
{
"from": "assistant",
"value": "<think> Ok... | [
"mulberry_images/geoqa_plus/5131.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194837 | [
{
"from": "user",
"value": "<image>In the given figure, a conical chimney cap is made of iron sheet, with a height of 30.0 and a bottom diameter of 80.0. Excluding processing residual materials, what is the minimum area of iron sheet required?\nChoices:\nA: 4000π(cm^{2})\nB: 2400π(cm^{2})\nC: 2000π(cm^{2})\... | [
"mulberry_images/geoqa_plus/2282.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194838 | [
{
"from": "user",
"value": "<image>In the provided figure, if a sector-shaped paper with a central angle measuring 120.0 degrees and a radius of 9.0 is used to create a conical bottomless paper cap, what will be the height of the cap?\nChoices:\nA: √{2}cm\nB: 3√{2}cm\nC: 4√{2}cm\nD: 6√{2}cm"
},
{
"f... | [
"mulberry_images/geoqa_plus/2106.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194839 | [
{
"from": "user",
"value": "<image>If the diagram shows triangle ABC with DE parallel to BC, and intersecting AB and AC at D and E, where AE equals 3.0 and EC equals 6.0, what is the value of frac ADAB?\nChoices:\nA: \\frac{1}{2}\nB: \\frac{1}{3}\nC: \\frac{1}{4}\nD: \\frac{1}{6}"
},
{
"from": "ass... | [
"mulberry_images/geoqa_plus/4526.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194840 | [
{
"from": "user",
"value": "<image>When it comes to covering a certain plane figure, we refer to the smallest circle that can completely enclose it as the smallest circle of the plane figure. If a rectangle with length 8.0 and width 6.0 is considered, what is the radius of its minimum covering circle?\nChoi... | [
"mulberry_images/geoqa_plus/1651.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194841 | [
{
"from": "user",
"value": "<image>If the time on a clock is 8:30, what is the degree measure of the angle formed by the hour hand and the minute hand?\nChoices:\nA: 30°\nB: 60°\nC: 75°\nD: 90°"
},
{
"from": "assistant",
"value": "<think> Okay, so the question is asking for the angle between the... | [
"mulberry_images/geoqa_plus/4936.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194842 | [
{
"from": "user",
"value": "<image>What is the diameter of the bottom of the cone when it is enclosed by a sector with a central angle of 120.0 and a radius of 9.0 (disregarding the joints)? \nChoices:\nA: 3\nB: 6\nC: 9\nD: 12"
},
{
"from": "assistant",
"value": "<think> Okay, so I need to find ... | [
"mulberry_images/geoqa_plus/2195.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194843 | [
{
"from": "user",
"value": "<image>Given that lines a and b are parallel and angle 1 measures 55 degrees, what is the degree measure of angle 2 in the figure shown?\nChoices:\nA: 115°\nB: 120°\nC: 125°\nD: 135°"
},
{
"from": "assistant",
"value": "<think> Okay, let's see. The problem illustrates... | [
"mulberry_images/geoqa_plus/1563.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194844 | [
{
"from": "user",
"value": "<image>If the three vertices of triangle ABD lie on circle O, with AB as the diameter and point C also lying on circle O, what is the degree measure of angle BCD if angle ABD is 52 degrees?\nChoices:\nA: 32°\nB: 38°\nC: 52°\nD: 66°"
},
{
"from": "assistant",
"value": ... | [
"mulberry_images/geoqa_plus/231.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194845 | [
{
"from": "user",
"value": "<image>In the provided figure, we see a rectangle labeled ABCD. The diagonals AC and BD intersect at point O. From point A, a perpendicular line AE is drawn to BD, intersecting it at point E. The ratio of BE to ED is 0.333333. Another perpendicular line OF is drawn from point O t... | [
"mulberry_images/geoqa_plus/12937.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194846 | [
{
"from": "user",
"value": "<image>In triangle ABC, when angle C measures 90°, angle A measures 30°, and side BC measures 4 units, and the midpoints of sides AC and AB are represented by points D and E respectively, if segment DE is connected and extended to a new point labeled F in such a way that segment ... | [
"mulberry_images/geoqa_plus/12959.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194847 | [
{
"from": "user",
"value": "<image>In the diagram showing circle O, where AB serves as the diameter and angle BAC is established as 40 degrees, what is the measure of angle ADC?\nChoices:\nA: 40°\nB: 50°\nC: 60°\nD: 90°"
},
{
"from": "assistant",
"value": "<think> Okay, so I need to find the mea... | [
"mulberry_images/geoqa_plus/1893.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194848 | [
{
"from": "user",
"value": "<image>In the provided figure of an expanded cone-shaped paper cup, with the bottom surface having a radius of 5.0 and the generatrix measuring 15.0, what is the lateral area of the paper cup?\nChoices:\nA: 75πcm^{2}\nB: 150πcm^{2}\nC: \\frac{75π}{2}cm^{2}\nD: \\frac{375π}{2}cm^{... | [
"mulberry_images/geoqa_plus/2054.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194849 | [
{
"from": "user",
"value": "<image>In the presented figure, Xiao Hua undertook the task of measuring the height of the building he resides in. Seeking support from his classmates, they collectively measured their shadow lengths at the same time, obtaining values of 0.5 for Xiao Hua and 15.0 for the building... | [
"mulberry_images/geoqa_plus/2389.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194850 | [
{
"from": "user",
"value": "<image>Xiaofang and her father are depicted in the picture, with her father standing at a height of 1.8 meters and casting a 2.1-meter shadow on the ground. If Xiaofang is 0.3 meters shorter than her father, what will be the length of her shadow?\nChoices:\nA: 1.3m\nB: 1.65m\nC: ... | [
"mulberry_images/geoqa_plus/2464.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194851 | [
{
"from": "user",
"value": "<image>Considering the rectangle ABCD depicted in the figure, with diagonals AC and BD intersecting at point O, if angle ABO measures 60° and the length of the diagonals is 6, what is the length of segment AD?\nChoices:\nA: 3√{3}\nB: 4\nC: 2√{3}\nD: 3"
},
{
"from": "assis... | [
"mulberry_images/geoqa_plus/12926.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194852 | [
{
"from": "user",
"value": "<image>Let triangle ABC be inscribed in circle O, as illustrated in the figure. Connecting points OA and OB, if angle ABO is equal to 40 degrees, what is the measure of angle C?\nChoices:\nA: 100°\nB: 80°\nC: 50°\nD: 40°"
},
{
"from": "assistant",
"value": "<think> Al... | [
"mulberry_images/geoqa_plus/1838.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194853 | [
{
"from": "user",
"value": "<image>What is the value of the radius of the bottom surface of the cone depicted in the figure if the length of the generatrix is 10.0 units and the expanded figure of the lateral surface can be represented as a sector with a central angle of 216.0 degrees?\nChoices:\nA: 3\nB: 6... | [
"mulberry_images/geoqa_plus/2085.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194854 | [
{
"from": "user",
"value": "<image>In the scenario where a cone-shaped paper cap is formed using a sector-shaped piece of paper with a central angle of 120.0 and a radius of 9.0, what will be the height of the cap? \nChoices:\nA: 6√{2}cm\nB: 6cm\nC: 6√{3}cm\nD: 6√{5}cm"
},
{
"from": "assistant",
... | [
"mulberry_images/geoqa_plus/2134.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194855 | [
{
"from": "user",
"value": "<image>In the given figure, angle CAB is measured at 70 degrees, and points A, B, and C are all on circle O. What is the degree measure of angle COB?\nChoices:\nA: 70°\nB: 80°\nC: 120°\nD: 140°"
},
{
"from": "assistant",
"value": "<think> Okay, so I need to find the m... | [
"mulberry_images/geoqa_plus/2278.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194856 | [
{
"from": "user",
"value": "<image>Consider the figure illustrating a square ABCD, where E lies on one of its diagonals. The quadrilateral EFCG is a rectangle. If the side length of square ABCD is 4 units, what is the total length of EG and GC?\nChoices:\nA: 4\nB: 8\nC: 16\nD: 32"
},
{
"from": "assi... | [
"mulberry_images/geoqa_plus/12472.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194857 | [
{
"from": "user",
"value": "<image>In the illustration of triangle ABC, E and F lie on AB and AC, respectively, and EF is parallel to BC. If EB/AB is 4/5, what is AC/FC?\nChoices:\nA: \\frac{9}{4}\nB: \\frac{5}{9}\nC: \\frac{5}{4}\nD: \\frac{9}{5}"
},
{
"from": "assistant",
"value": "<think> Oka... | [
"mulberry_images/geoqa_plus/4760.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194858 | [
{
"from": "user",
"value": "<image>In the given figure, in a right triangle ABC where angle ACB is 90° and AB measures 13, the midpoints of AB and AC are labeled D and E. If the length of DE is 2.5, what would be the perimeter of triangle BCD? \nChoices:\nA: 13\nB: 14.5\nC: 15.5\nD: 18"
},
{
"from":... | [
"mulberry_images/geoqa_plus/13022.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194859 | [
{
"from": "user",
"value": "<image>In the shown figure, if BC represents the diameter of a circle and angle ABC is 35 degrees, what is the degree measure of angle D?\nChoices:\nA: 35°\nB: 45°\nC: 55°\nD: 65°"
},
{
"from": "assistant",
"value": "<think> Okay, let me try to figure this out. So, th... | [
"mulberry_images/geoqa_plus/1784.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194860 | [
{
"from": "user",
"value": "<image>In the given figure, a large parasol is displayed. When the umbrella surface is expanded, it takes the shape of a cone. The length of the generatrix of this cone is given as 5.0 units and the radius of the base is 3.0 units. How much fabric area is needed to manufacture th... | [
"mulberry_images/geoqa_plus/2164.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194861 | [
{
"from": "user",
"value": "<image>In the provided picture, a cone with a base radius of 1.0 and a height of 2.0 can be seen. What is the measurement of its lateral area?\nChoices:\nA: √{3}\nB: √{3}π\nC: √{5}π\nD: √{5}"
},
{
"from": "assistant",
"value": "<think> Okay, let me try to figure this ... | [
"mulberry_images/geoqa_plus/2193.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194862 | [
{
"from": "user",
"value": "<image>If in the given diagram, quadrilateral ABCD is depicted with AB parallel to CD and the lengths of AB, AC, AD all equal to 4.0 while BC measures 2.0, then what is the measurement of BD?\nChoices:\nA: √{62}\nB: 2√{15}\nC: 2√{10}\nD: 2√{5}"
},
{
"from": "assistant",
... | [
"mulberry_images/geoqa_plus/1733.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194863 | [
{
"from": "user",
"value": "<image>Assuming that circle O is the circumcircle of triangle ABC and angle C is 35.0 degrees, what is the value of angle OBA?\nChoices:\nA: 50°\nB: 60°\nC: 70°\nD: 55°"
},
{
"from": "assistant",
"value": "<think> Okay, let's try to figure this out. So, we have triang... | [
"mulberry_images/geoqa_plus/1763.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194864 | [
{
"from": "user",
"value": "<image>Find the smallest possible length of EF in the provided diagram, which shows triangle ABC with a 90° angle at A. Given that AC measures 8 units and AB measures 6 units, point D is a movable point on side BC (excluding points B and C). D is the point where DE is perpendicul... | [
"mulberry_images/geoqa_plus/12936.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194865 | [
{
"from": "user",
"value": "<image>Given that Liangliang made a cone-shaped paper hat out of cardboard for the 10th Lanzhou Primary and Middle School Students' Art Festival, with a bottom radius of 9.0 and a height of 12.0, what is the lateral area of the conical paper cap without accounting for any loss?\n... | [
"mulberry_images/geoqa_plus/2125.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194866 | [
{
"from": "user",
"value": "<image>Triangle ABC is depicted in the figure provided, and it is a right triangle with angle ACB equal to 90.0 degrees. The line segment CD represents the length of the altitude drawn from side AB. If the lengths of AB, AC, and BC are 5.0, 4.0, and 3.0 respectively, what is the ... | [
"mulberry_images/geoqa_plus/1960.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194867 | [
{
"from": "user",
"value": "<image>In triangle ABC, if AD = 3.0, DB = 2.0, and DE is parallel to BC, what is the relationship between the length of DE and BC?\nChoices:\nA: \\frac{3}{2}\nB: \\frac{2}{3}\nC: \\frac{9}{4}\nD: \\frac{3}{5}"
},
{
"from": "assistant",
"value": "<think> Okay, let's se... | [
"mulberry_images/geoqa_plus/4731.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194868 | [
{
"from": "user",
"value": "<image>Consider the given figure, presenting a \"Zhao Shuang Chord Diagram\" obtained by combining four congruent right-angled triangles: triangle ABE, triangle BCF, triangle CDG, and triangle DAH. The combined area of these triangles is stated to be 24 square units. In this cont... | [
"mulberry_images/geoqa_plus/12064.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194869 | [
{
"from": "user",
"value": "<image>Within the depicted figure, two straight lines, n, are intersected by three parallel lines a, b, and c, creating intersection points A, C, and F, and B, D, and E. If AF has a length of 10.0, AC is 4.0, and BE measures 12.0, what is the length of DE?\nChoices:\nA: 4\nB: 6\n... | [
"mulberry_images/geoqa_plus/4631.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194870 | [
{
"from": "user",
"value": "<image>As shown in the figure, consider the situation where line a is parallel to line b and line AC is perpendicular to line AB. The intersection of line AC and line b is at point C. If angle 1 is measured as 60 degrees, what is the degree measurement of angle 2?\nChoices:\nA: 5... | [
"mulberry_images/geoqa_plus/1534.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194871 | [
{
"from": "user",
"value": "<image>When a trolley drives up a slope with an inclination angle α, covering a distance of 13.0, and sinα equals 5.0/13.0, what is the height of the ascent for the trolley, as shown in the figure?\nChoices:\nA: 5米\nB: 6米\nC: 6.5米\nD: 7米"
},
{
"from": "assistant",
"va... | [
"mulberry_images/geoqa_plus/5515.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194872 | [
{
"from": "user",
"value": "<image>In the given figure, with points A, B, and C lying on circle O and the degree of arc ACB set at 300 degrees, what is the degree measure of angle C?\nChoices:\nA: 30°\nB: 40°\nC: 50°\nD: 60°"
},
{
"from": "assistant",
"value": "<think> Okay, let's see. So the pr... | [
"mulberry_images/geoqa_plus/1745.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194873 | [
{
"from": "user",
"value": "<image>Provided that the C island is situated at a position 45.0 degrees north by east of the A island and 25.0 degrees north by west of the B island in the given figure, what is the degree of angle ACB, representing the view from the C island to the A and B islands?\nChoices:\nA... | [
"mulberry_images/geoqa_plus/148.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194874 | [
{
"from": "user",
"value": "<image>If in circle O, chords AB and CD intersect perpendicularly at point P, and angle A has a measure of 35 degrees, what is the measure of angle B?\nChoices:\nA: 35°\nB: 55°\nC: 65°\nD: 70°"
},
{
"from": "assistant",
"value": "<think> Okay, so I need to figure out ... | [
"mulberry_images/geoqa_plus/1802.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194875 | [
{
"from": "user",
"value": "<image>As depicted in the figure, in quadrilateral ABCD with angle C measured at 108 degrees, if line segment BE serves as the bisector of angle ABC, what is the degree value of angle AEB?\nChoices:\nA: 18°\nB: 36°\nC: 72°\nD: 108°"
},
{
"from": "assistant",
"value": ... | [
"mulberry_images/geoqa_plus/1616.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194876 | [
{
"from": "user",
"value": "<image>Consider the figure provided, where AB represents the diameter of circle O. Points C and D lie on the circumference of circle O, and CD is perpendicular to AB. If angle DAB is measured at 65.0 degrees, what is the degree measure of angle AOC?\nChoices:\nA: 25°\nB: 30°\nC: ... | [
"mulberry_images/geoqa_plus/133.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194877 | [
{
"from": "user",
"value": "<image>Given a conical chimney cap made of iron sheet as shown in the figure, with a height of 30.0 and a bottom diameter of 80.0, what is the minimum area of iron sheet required, excluding processing residual materials?\nChoices:\nA: 4000π(cm^{2})\nB: 2400π(cm^{2})\nC: 2000π(cm^... | [
"mulberry_images/geoqa_plus/2282.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194878 | [
{
"from": "user",
"value": "<image>What is the base radius of the cone formed when using a sector-shaped piece of paper with a radius of 10.0 and a central angle of 144.0?\nChoices:\nA: 3\nB: 4\nC: 5\nD: 6"
},
{
"from": "assistant",
"value": "<think> Okay, let's see. The problem is about a secto... | [
"mulberry_images/geoqa_plus/2219.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194879 | [
{
"from": "user",
"value": "<image>Angle C in the provided figure is part of a triangle ABC. AD is the bisector of angle EAC, parallel to BC, and angle B measures 35.0 degrees. What is the degree measure of angle C?\nChoices:\nA: 55°\nB: 45°\nC: 35°\nD: 25°"
},
{
"from": "assistant",
"value": "<... | [
"mulberry_images/geoqa_plus/487.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194880 | [
{
"from": "user",
"value": "<image>In the provided figure, circle O is shown with diameter AB forming a right angle with CD at point E. If angle BOD measures 48.0 degrees, what is the degree measure of angle BAC?\nChoices:\nA: 60°\nB: 48°\nC: 30°\nD: 24°"
},
{
"from": "assistant",
"value": "<thi... | [
"mulberry_images/geoqa_plus/211.png"
] | vision_r1_mulberry_sft_full |
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