id stringlengths 29 36 | conversations listlengths 1 48 | images listlengths 1 1 | source_dataset stringclasses 2
values |
|---|---|---|---|
vision_r1_mulberry_sft_full-194881 | [
{
"from": "user",
"value": "<image>What is the length of the shadow formed by student A when two students from Class A and B of Grade 9 are positioned at points C and D respectively during a physical education class? It is known that the shadow of student B lies completely within the shadow of student A. Th... | [
"mulberry_images/geoqa_plus/2355.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194882 | [
{
"from": "user",
"value": "<image>In the diagram, the point of intersection of the diagonals of parallelogram ABCD is labeled O. It is also given that AD and CD have different lengths, and that OM is perpendicular to AC, intersecting AD at point M. If the perimeter of triangle CDM is 5, what is the perimet... | [
"mulberry_images/geoqa_plus/13099.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194883 | [
{
"from": "user",
"value": "<image>Given the figure, where circle O is depicted with diameter AB measuring 10.0 units and chord BC measuring 6.0 units, point D is the perpendicular foot from OD to AC. What is the measurement of OD?\nChoices:\nA: 6\nB: 5\nC: 4\nD: 3"
},
{
"from": "assistant",
"va... | [
"mulberry_images/geoqa_plus/1814.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194884 | [
{
"from": "user",
"value": "<image>If the bottom radius of the cone is 6.0 and the height CO is 8.0, then what is the measure of the central angle of the expanded figure of the lateral surface of the cone?\nChoices:\nA: 120°\nB: 180°\nC: 216°\nD: 236°"
},
{
"from": "assistant",
"value": "<think>... | [
"mulberry_images/geoqa_plus/2130.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194885 | [
{
"from": "user",
"value": "<image>Consider the diagram with triangle ABC and point D inside it. BD is perpendicular to CD and E, F, G, and H are the midpoints of sides AB, BD, CD, and AC respectively. If AD = 10, BD = 8, and CD = 6, what is the perimeter of quadrilateral EFGH?\nChoices:\nA: 24\nB: 20\nC: 1... | [
"mulberry_images/geoqa_plus/12981.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194886 | [
{
"from": "user",
"value": "<image>In the given figure, triangle ABC is enclosed within circle O. Connect points OA and OB. If angle ABO measures 40 degrees, determine the degree measure of angle C.\nChoices:\nA: 100°\nB: 80°\nC: 50°\nD: 40°"
},
{
"from": "assistant",
"value": "<think> Okay, let... | [
"mulberry_images/geoqa_plus/1838.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194887 | [
{
"from": "user",
"value": "<image>Given a sector with a central angle of 120.0 and a radius of 9.0, what is the bottom diameter of the cone formed when the sector encloses the cone (without considering the joints)? \nChoices:\nA: 3\nB: 6\nC: 9\nD: 12"
},
{
"from": "assistant",
"value": "<think>... | [
"mulberry_images/geoqa_plus/2195.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194888 | [
{
"from": "user",
"value": "<image>In the diagram shown, circle O is depicted with diameters AB and CD. Chords DF and BE are drawn such that the measures of arc DF and arc BE are equal. With angle B measuring 50.0 degrees, what is the degree measure of angle D?\nChoices:\nA: 25°\nB: 40°\nC: 50°\nD: 60°"
}... | [
"mulberry_images/geoqa_plus/1695.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194889 | [
{
"from": "user",
"value": "<image>If in the given diagram AB is parallel to CD and CB is perpendicular to DB, with angle D measuring 65.0 degrees, what is the size of angle ABC?\nChoices:\nA: 25°\nB: 35°\nC: 50°\nD: 65°"
},
{
"from": "assistant",
"value": "<think> Okay, let me try to figure thi... | [
"mulberry_images/geoqa_plus/210.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194890 | [
{
"from": "user",
"value": "<image>In the figure, where the quadrilateral ABCD is inscribed within circle O and angle BCD is 120 degrees, how much does angle BOD measure?\nChoices:\nA: 80°\nB: 90°\nC: 100°\nD: 120°"
},
{
"from": "assistant",
"value": "<think> Okay, so there's a quadrilateral ABC... | [
"mulberry_images/geoqa_plus/1322.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194891 | [
{
"from": "user",
"value": "<image>In the provided picture, Liangliang constructed a cone-shaped paper hat using cardboard for the 10th Lanzhou Primary and Middle School Students' Art Festival. The cone has a bottom radius of 9.0 and a height of 12.0. What is the lateral area of the conical paper cap, not c... | [
"mulberry_images/geoqa_plus/2125.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194892 | [
{
"from": "user",
"value": "<image>In the diagram provided, a cross section of a sewage pipe is shown. The radius of the cross section, OB, is indicated to be 5.0, and the distance from the center O to the sewage surface, OC, is given as 3.0. What is the exact width of the sewage surface, AB?\nChoices:\nA: ... | [
"mulberry_images/geoqa_plus/1940.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194893 | [
{
"from": "user",
"value": "<image>Within triangle ABC, a perpendicular line AD is drawn from point A to the angle bisector of angle ABC. This line intersects the angle bisector at point P and side BC at point D. If the area of triangle ABP is 4 and the area of triangle CDP is 2, what is the area of triangl... | [
"mulberry_images/geoqa_plus/11811.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194894 | [
{
"from": "user",
"value": "<image>The diagram depicts Xiao Ming's devised flashlight arrangement for measuring the height of an ancient city wall, with a horizontal plane mirror located at point P. The light emitted from point A is reflected by the plane mirror and directly hits the top C of the ancient ci... | [
"mulberry_images/geoqa_plus/2460.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194895 | [
{
"from": "user",
"value": "<image>In the given figure, the conical Christmas hat has a generatrix length of 2.0 and a bottom radius of 1.0. What is the value of its lateral area? \nChoices:\nA: 2\nB: π\nC: 2π\nD: 4π"
},
{
"from": "assistant",
"value": "<think> Okay, let's see. The problem is ab... | [
"mulberry_images/geoqa_plus/2190.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194896 | [
{
"from": "user",
"value": "<image>Given that the generatrix length of the cone mold is 10.0 and the bottom radius is 5.0, what is the lateral area of the cone mold?\nChoices:\nA: 10π\nB: 50π\nC: 100π\nD: 150π"
},
{
"from": "assistant",
"value": "<think> Okay, let's see. The problem is about fin... | [
"mulberry_images/geoqa_plus/192.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194897 | [
{
"from": "user",
"value": "<image>Liangliang created a cone-shaped paper hat using cardboard for the 10th Lanzhou Primary and Middle School Students' Art Festival. The picture shows that the bottom radius of the cone is 9.0 and the height is 12.0. What is the lateral area of the conical paper cap, disregar... | [
"mulberry_images/geoqa_plus/2125.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194898 | [
{
"from": "user",
"value": "<image>In the given figure, parallelogram ABCD undergoes a counterclockwise rotation of 30.0 degrees around point A, leading to the formation of parallelogram AB'C'D' (B' corresponding to B, C' corresponding to C, and D' corresponding to D). As a result of this rotation, point B'... | [
"mulberry_images/geoqa_plus/1418.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194899 | [
{
"from": "user",
"value": "<image>As depicted in the figure, AB runs parallel to CD, while AC and BD intersect at point O. Given that DO is 3.0, BO is 5.0, and DC is 4.0, what is the length of AB?\nChoices:\nA: 6\nB: 8\nC: \\frac{20}{3}\nD: \\frac{15}{4}"
},
{
"from": "assistant",
"value": "<th... | [
"mulberry_images/geoqa_plus/4634.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194900 | [
{
"from": "user",
"value": "<image>In the provided figure, with points A, B, and C lying on circle O and angle AOB measuring 60.0 degrees, what is the degree measure of angle ACB?\nChoices:\nA: 20°\nB: 30°\nC: 40°\nD: 60°"
},
{
"from": "assistant",
"value": "<think> Okay, so there's this geometr... | [
"mulberry_images/geoqa_plus/1896.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194901 | [
{
"from": "user",
"value": "<image>In the figure showing triangle ABC, point M serves as the midpoint of BC, while AN bisects the angle BAC and BN is perpendicular to AN. When AB equals 14 and AC equals 19, what is the measurement of MN?\nChoices:\nA: 2\nB: 2.5\nC: 3\nD: 3.5"
},
{
"from": "assistant... | [
"mulberry_images/geoqa_plus/13058.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194902 | [
{
"from": "user",
"value": "<image>In the diagram provided, line a is parallel to line b. If angle 1 is found to measure 75.0 degrees and angle 2 measures 35.0 degrees, what would be the degree measure of angle 3?\nChoices:\nA: 75°\nB: 55°\nC: 40°\nD: 35°"
},
{
"from": "assistant",
"value": "<th... | [
"mulberry_images/geoqa_plus/162.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194903 | [
{
"from": "user",
"value": "<image>Given the diagram, where point P is external to circle O and PA is a tangent to circle O at point A, intersecting line PO at point B, with angle P measuring 30 degrees, if BP measures 4 units, what is the length of segment AP?\nChoices:\nA: 4\nB: 8\nC: 4√{3}\nD: 4√{2}"
}... | [
"mulberry_images/geoqa_plus/12653.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194904 | [
{
"from": "user",
"value": "<image>When trying to measure the height of a flagpole on campus, Xiaohu found that his height is 1.6, and his shadow length is 2.0. Given that the flagpole's shadow length is 20.0, what is the height of the flagpole?\nChoices:\nA: 8\nB: 10\nC: 20\nD: 16"
},
{
"from": "as... | [
"mulberry_images/geoqa_plus/2400.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194905 | [
{
"from": "user",
"value": "<image>How long is the distance from chord AB to the center OE, when the radius of circle O is 2.0 and the length of chord AB is 2.0√{3.0}?\nChoices:\nA: \\frac{1}{2}\nB: √{3}\nC: 1\nD: √{2}"
},
{
"from": "assistant",
"value": "<think> Okay, let's see. The problem is ... | [
"mulberry_images/geoqa_plus/5216.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194906 | [
{
"from": "user",
"value": "<image>Given a sector with a radius of 30.0 and a central angle of 120.0 being transformed into the lateral surface of a cone, what will be the radius of the cone's base?\nChoices:\nA: 10cm\nB: 20cm\nC: 10πcm\nD: 20πcm"
},
{
"from": "assistant",
"value": "<think> Okay... | [
"mulberry_images/geoqa_plus/2018.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194907 | [
{
"from": "user",
"value": "<image>Consider the figure, where circle O has a radius of 3.0 units and points A, B, C, and D are positioned on it. If OA is perpendicular to BC and angle CDA measures 30.0 degrees, what is the length of chord BC?\nChoices:\nA: \\frac{3√{3}}{2}\nB: 3√{3}\nC: 3\nD: 2√{3}"
},
... | [
"mulberry_images/geoqa_plus/1754.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194908 | [
{
"from": "user",
"value": "<image>If the standard eye chart with a test distance of 5.0 has a length of \"E\" equal to 3.6, what will be the length of the corresponding \"E\" in the eye chart with a test distance of 3.0?\nChoices:\nA: 1.44cm\nB: 2.16cm\nC: 2.4cm\nD: 3.6cm"
},
{
"from": "assistant",... | [
"mulberry_images/geoqa_plus/2293.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194909 | [
{
"from": "user",
"value": "<image>In the provided figure of circle O, if angle ACB is measured at 50 degrees and angle AOC is measured at 60 degrees, what is the degree measure of angle BAC?\nChoices:\nA: 95°\nB: 100°\nC: 105°\nD: 110°"
},
{
"from": "assistant",
"value": "<think> Okay, so I nee... | [
"mulberry_images/geoqa_plus/1891.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194910 | [
{
"from": "user",
"value": "<image>In the diagram showing quadrilateral ABCD, where P is the midpoint of diagonal BD, and E and F indicate the midpoints of sides AB and CD, respectively, and with AD equal to BC, when angle PEF measures 25 degrees, what is the degree of angle EPF?\nChoices:\nA: 100°\nB: 120°... | [
"mulberry_images/geoqa_plus/1316.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194911 | [
{
"from": "user",
"value": "<image>Given that AD is the diameter of circle O and has a length of 8 cm, and angle DAC is equal to angle ABC, what is the measurement 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 to figure... | [
"mulberry_images/geoqa_plus/13109.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194912 | [
{
"from": "user",
"value": "<image>The figure depicts a conical Christmas hat with a generatrix length of 2.0 and a bottom radius of 1.0. Determine the lateral area of the hat. \nChoices:\nA: 2\nB: π\nC: 2π\nD: 4π"
},
{
"from": "assistant",
"value": "<think> Okay, let's see. The problem is about... | [
"mulberry_images/geoqa_plus/2190.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194913 | [
{
"from": "user",
"value": "<image>In the figure provided, circle O has a diameter AE, which is known to be 10.0 units. Moreover, it is stated that angle B is equal to angle EAC. What is the length of AC in this scenario?\nChoices:\nA: 5cm\nB: 5√{2}cm\nC: 5√{3}cm\nD: 6cm"
},
{
"from": "assistant",
... | [
"mulberry_images/geoqa_plus/1900.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194914 | [
{
"from": "user",
"value": "<image>How was the measurement scheme designed by the school mathematics interest group, employing a mirror and a measuring tape, to measure the height of an inaccessible tree on the level of the campus?\nChoices:\nA: 2.8米\nB: 5.6米\nC: 8.6米\nD: 9.2米"
},
{
"from": "assista... | [
"mulberry_images/geoqa_plus/2462.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194915 | [
{
"from": "user",
"value": "<image>If angle BOC measures 72.0 degrees and points A, B, and C are all on circle O, what is the measure of angle BAC?\nChoices:\nA: 72°\nB: 36°\nC: 18°\nD: 54°"
},
{
"from": "assistant",
"value": "<think> Okay, so there's this circle with center O, and points A, B, ... | [
"mulberry_images/geoqa_plus/1905.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194916 | [
{
"from": "user",
"value": "<image>In the provided figure, if a right triangle plate with 45.0 angles is positioned on the opposite sides of a ruler and angle 1 measures 20.0 degrees, what is the degree measure of angle 2?\nChoices:\nA: 30°\nB: 25°\nC: 20°\nD: 15°"
},
{
"from": "assistant",
"val... | [
"mulberry_images/geoqa_plus/1552.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194917 | [
{
"from": "user",
"value": "<image>Given that points A, B, and C lie on circle O and angle ACB is 112.0 degrees, what is the measure of angle α? \nChoices:\nA: 68°\nB: 112°\nC: 136°\nD: 134°"
},
{
"from": "assistant",
"value": "<think> Okay, so there's a circle with center O and points A, B, C o... | [
"mulberry_images/geoqa_plus/1755.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194918 | [
{
"from": "user",
"value": "<image>What is the lateral area of a cone with a radius of 3.0 and a height of 4.0?\nChoices:\nA: 12π\nB: 15π\nC: 24π\nD: 30π"
},
{
"from": "assistant",
"value": "<think> Okay, let's tackle this problem step by step. The question is asking for the lateral area of a co... | [
"mulberry_images/geoqa_plus/2010.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194919 | [
{
"from": "user",
"value": "<image>Given that the distance between the midpoint M on one side and the diagonal intersection O of diamond ABCD is 5.0, determine the perimeter of the diamond.\nChoices:\nA: 5cm\nB: 10cm\nC: 20cm\nD: 40cm"
},
{
"from": "assistant",
"value": "<think> Okay, let me try... | [
"mulberry_images/geoqa_plus/1556.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194920 | [
{
"from": "user",
"value": "<image>The bisector of angle A intersects CD at point E in parallelogram ABCD as shown in the figure. Given that AB measures 5 and BC measures 3, what is the length of EC?\nChoices:\nA: 1\nB: 1.5\nC: 2\nD: 3"
},
{
"from": "assistant",
"value": "<think> Okay, so we hav... | [
"mulberry_images/geoqa_plus/13100.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194921 | [
{
"from": "user",
"value": "<image>With the generatrix length of the cone mold measuring 10.0 and the bottom radius set at 5.0, what is the amount of lateral area encompassed by the cone mold?\nChoices:\nA: 10π\nB: 50π\nC: 100π\nD: 150π"
},
{
"from": "assistant",
"value": "<think> Okay, let's se... | [
"mulberry_images/geoqa_plus/192.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194922 | [
{
"from": "user",
"value": "<image>Considering a sector-shaped piece of paper with a central angle measuring 120.0 and a radius of 9.0, when it is utilized to create a paper cap with a conical shape (disregarding the seam), what value will represent the height of the cap? \nChoices:\nA: 6√{2}cm\nB: 6cm\nC: ... | [
"mulberry_images/geoqa_plus/2134.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194923 | [
{
"from": "user",
"value": "<image>In the scenario where a sector with a radius of 9.0 and a central angle of 120.0 is utilized to enclose the lateral surface of a cone (ignoring the joints), what value does the base radius of the cone hold?\nChoices:\nA: 9\nB: 3\nC: 1\nD: 6"
},
{
"from": "assistant... | [
"mulberry_images/geoqa_plus/2037.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194924 | [
{
"from": "user",
"value": "<image>In the provided diagram, we have two concentric circles with radii measuring 4.0 and 5.0 units respectively. Additionally, a chord AB of the larger circle is tangent to the smaller circle. What is the length of chord AB?\nChoices:\nA: 3cm\nB: 4cm\nC: 6cm\nD: 8cm"
},
{
... | [
"mulberry_images/geoqa_plus/2.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194925 | [
{
"from": "user",
"value": "<image>In the provided figure, angles ABC and AOC are located on circle O. If 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 there's this circle with cen... | [
"mulberry_images/geoqa_plus/1881.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194926 | [
{
"from": "user",
"value": "<image>The given figure depicts triangle ABC, where angle A is measured at 70.0 degrees. Point O is the point of intersection of the perpendicular bisectors of sides AB and AC. Calculate the degree measurement of angle BCO.\nChoices:\nA: 40°\nB: 30°\nC: 20°\nD: 10°"
},
{
... | [
"mulberry_images/geoqa_plus/1516.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194927 | [
{
"from": "user",
"value": "<image>Given the provided figure, where circle O has a diameter measuring 12.0 units and the length of segment AB is also 12.0 units, chord CD is drawn within the circle such that AB is perpendicular to CD and the foot of the perpendicular is labeled as point E. If angle BOC meas... | [
"mulberry_images/geoqa_plus/5110.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194928 | [
{
"from": "user",
"value": "<image>Given that the chord AB of circle O has a length of 18.0 units and that M is the midpoint of AB, with OM measuring 12.0 units, what is the value of the radius of circle O?\nChoices:\nA: 8\nB: 2\nC: 10\nD: 15"
},
{
"from": "assistant",
"value": "<think> Okay, le... | [
"mulberry_images/geoqa_plus/5122.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194929 | [
{
"from": "user",
"value": "<image>In order to estimate the width of the river, a target point is selected on the opposite bank and labeled as point A, while points B and C are selected on this side of the river such that AB is perpendicular to BC. Additionally, a point E is chosen on the river bank, where ... | [
"mulberry_images/geoqa_plus/2310.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194930 | [
{
"from": "user",
"value": "<image>Given that the radius of the bottom surface of the cone is 3.0 and the height is 4.0, what is the lateral area of the cone, as depicted in the figure?\nChoices:\nA: 10πcm^{2}\nB: 15πcm^{2}\nC: 20πcm^{2}\nD: 25πcm^{2}"
},
{
"from": "assistant",
"value": "<think>... | [
"mulberry_images/geoqa_plus/2230.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194931 | [
{
"from": "user",
"value": "<image>If AD is parallel to BC in the trapezoid ABCD and E and F are the midpoints of the diagonals BD and AC, respectively, what is the length of EF if AD measures 6.0 and BC measures 18.0?\nChoices:\nA: 8cm\nB: 7cm\nC: 6cm\nD: 5cm"
},
{
"from": "assistant",
"value":... | [
"mulberry_images/geoqa_plus/4969.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194932 | [
{
"from": "user",
"value": "<image>Given that the railroad crossing railing has a short arm with a length of 1.0 and a long arm with a length of 12.0, what will be the change in position of the end of the long arm if the end of the short arm is lowered by 0.5 as shown in the figure?\nChoices:\nA: 6米\nB: 8米\... | [
"mulberry_images/geoqa_plus/2437.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194933 | [
{
"from": "user",
"value": "<image>If angle CAB measures 70 degrees and points A, B, and C are on circle O, what is the size of angle COB?\nChoices:\nA: 70°\nB: 80°\nC: 120°\nD: 140°"
},
{
"from": "assistant",
"value": "<think> Okay, let's see. The problem shows angle CAB is 70 degrees, and poin... | [
"mulberry_images/geoqa_plus/2278.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194934 | [
{
"from": "user",
"value": "<image>Consider the figure where quadrilateral ABCD is inscribed within circle O and angle B is measured at 70.0 degrees. What is the numerical value of angle D?\nChoices:\nA: 110°\nB: 90°\nC: 70°\nD: 50°"
},
{
"from": "assistant",
"value": "<think> Okay, so there's t... | [
"mulberry_images/geoqa_plus/229.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194935 | [
{
"from": "user",
"value": "<image>The figure illustrates circle O, with diameter AB, and point C situated on the circle. CD is depicted as a line that intersects AB perpendicularly at point D. If the lengths of AB and BC are 10.0 and 6.0 respectively, what is the numerical value of CD?\nChoices:\nA: 1.2\nB... | [
"mulberry_images/geoqa_plus/1918.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194936 | [
{
"from": "user",
"value": "<image>What is the radius at the base of the cone if a sector with a radius of 9.0 and a central angle of 120.0 is used to wrap around the lateral surface of the cone, disregarding the joints?\nChoices:\nA: 9\nB: 3\nC: 1\nD: 6"
},
{
"from": "assistant",
"value": "<thi... | [
"mulberry_images/geoqa_plus/2037.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194937 | [
{
"from": "user",
"value": "<image>If points A, B, and C are situated on circle O and the measure of angle ABC is 40 degrees, what is the measure of angle AOC?\nChoices:\nA: 40°\nB: 50°\nC: 60°\nD: 80°"
},
{
"from": "assistant",
"value": "<think> Okay, so the problem is about a circle with cente... | [
"mulberry_images/geoqa_plus/1881.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194938 | [
{
"from": "user",
"value": "<image>In the given figure, where points A, B, and C are located on circle O, if the angle ACB measures 112.0 degrees, what is the degree value of angle α? \nChoices:\nA: 68°\nB: 112°\nC: 136°\nD: 134°"
},
{
"from": "assistant",
"value": "<think> Okay, let's see. The ... | [
"mulberry_images/geoqa_plus/1755.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194939 | [
{
"from": "user",
"value": "<image>In the figure depicting right triangle ABC with angle BAC at 90°, the midpoints of sides AB and BC are denoted as D and E, and point F is located on the extension of side CA. Given that angle FDA equals angle B, and the lengths of sides AC and AB are 6 and 8 respectively, ... | [
"mulberry_images/geoqa_plus/13072.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194940 | [
{
"from": "user",
"value": "<image>Given the information that AB is a chord in circle O, with the radius of the circle measuring 5.0 units and AB itself measuring 8.0 units, what is the length of OP if point P represents the midpoint of AB?\nChoices:\nA: 2\nB: 3\nC: 4\nD: 5"
},
{
"from": "assistant"... | [
"mulberry_images/geoqa_plus/5135.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194941 | [
{
"from": "user",
"value": "<image>In the provided figure, triangle ABC has AB, AD, and DC as equal measurements. Given that angle B is 70.0 degrees, what is the measure of angle C?\nChoices:\nA: 35°\nB: 40°\nC: 45°\nD: 50°"
},
{
"from": "assistant",
"value": "<think> Okay, let's see. So we have... | [
"mulberry_images/geoqa_plus/173.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194942 | [
{
"from": "user",
"value": "<image>Triangle ABC has DE parallel to BC and AD to DB in the ratio 1:3. What is the 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 step by s... | [
"mulberry_images/geoqa_plus/4752.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194943 | [
{
"from": "user",
"value": "<image>What is the radius of the bottom circle of the cone when a sector with a radius of 9.0 and a central angle of 120.0 is rolled into a cone (without overlap) as shown in the figure?\nChoices:\nA: 1\nB: 2\nC: 3\nD: π"
},
{
"from": "assistant",
"value": "<think> Ok... | [
"mulberry_images/geoqa_plus/2122.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194944 | [
{
"from": "user",
"value": "<image>When triangle ABC is shown in the figure, with angles ACB and ABC measuring 90 and 60 degrees respectively, the angle bisector of ABC intersects BD at point P, which is the midpoint of BD. Given that AD is equal to 6, what is the length of CP?\nChoices:\nA: 3\nB: 3.5\nC: 4... | [
"mulberry_images/geoqa_plus/12834.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194945 | [
{
"from": "user",
"value": "<image>In circle O, as shown in the figure, the diameter AB is perpendicular to chord CD, and the foot of the vertical is denoted by point P. What is the radius of the circle if CD measures 8.0 units and OP is 3.0 units long?\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-194946 | [
{
"from": "user",
"value": "<image>In the provided diagram, we can see that points A, B, and E are arranged in a straight line. Two squares, ABCD and BEFG, have side lengths equal to 6 and 8 units, respectively. Point H is the midpoint of the line segment DF. What is the length of BH?\nChoices:\nA: 6\nB: 8\... | [
"mulberry_images/geoqa_plus/12744.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194947 | [
{
"from": "user",
"value": "<image>Suppose a cone is created by using a sector-shaped piece of paper with a radius of 10.0 and a central angle of 144.0. What would be the measurement of the bottom radius of the cone?\nChoices:\nA: 3\nB: 4\nC: 5\nD: 6"
},
{
"from": "assistant",
"value": "<think> ... | [
"mulberry_images/geoqa_plus/2219.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194948 | [
{
"from": "user",
"value": "<image>Within the context of the right triangle ABC, with angle ACB measuring 90 degrees, points D and E are identified as the midpoints of sides AB and BC respectively. By extending AC to point F, where CF equals half the length of AC, and if the length of EF is known to be 4 un... | [
"mulberry_images/geoqa_plus/12840.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194949 | [
{
"from": "user",
"value": "<image>If in triangle ABC, point D lies on edge AB and the parallel line DE intersecting AC at point E, with AD/DB = 3.0/5.0 and AE = 6.0, what is the length of EC?\nChoices:\nA: 8\nB: 10\nC: 12\nD: 16"
},
{
"from": "assistant",
"value": "<think> Okay, let's see. So t... | [
"mulberry_images/geoqa_plus/4727.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194950 | [
{
"from": "user",
"value": "<image>Given that circle O is the circumcircle of triangle ABC and angle A is 72.0 degrees, what is the degree measurement of angle BCO?\nChoices:\nA: 15°\nB: 18°\nC: 20°\nD: 28°"
},
{
"from": "assistant",
"value": "<think> Okay, so I need to find the measure of angle... | [
"mulberry_images/geoqa_plus/236.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194951 | [
{
"from": "user",
"value": "<image>If a river's width is to be estimated accurately, the figure provided shows a target point A on the opposite bank of the river, along with points B, C, and D close to the bank. AB and CD are both perpendicular to BC, and E is a point along BC. Furthermore, points A, E, and... | [
"mulberry_images/geoqa_plus/2379.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194952 | [
{
"from": "user",
"value": "<image>What is the change in height at the end of the long arm when the end of the short arm of the railing at the railway crossing drops by 0.5, if the length of the short arm is 1.0 and the length of the long arm is 16.0?\nChoices:\nA: 5m\nB: 6m\nC: 7m\nD: 8m"
},
{
"fro... | [
"mulberry_images/geoqa_plus/2350.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194953 | [
{
"from": "user",
"value": "<image>Given the figure displaying triangle ABC with sides AB and AC measuring 10 and 6 units respectively, and point AD being the angle bisector while AE is the median. Additionally, CF is a line segment perpendicular to AD at point F, and EF is the line segment linking points E... | [
"mulberry_images/geoqa_plus/13004.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194954 | [
{
"from": "user",
"value": "<image>In the figure, angle 1 is measured at 100.0 degrees and angle C at 70.0 degrees. What is the degree measure of angle A?\nChoices:\nA: 10°\nB: 20°\nC: 30°\nD: 80°"
},
{
"from": "assistant",
"value": "<think> Okay, let me try to figure this out. So there's a tria... | [
"mulberry_images/geoqa_plus/52.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194955 | [
{
"from": "user",
"value": "<image>Given that right triangle ABC has angle BAC measuring 90 degrees, AB measuring 2.0 units, and BC measuring 5.0 units, when this triangle is rotated around the line AC, what will be the surface area of the resulting cone?\nChoices:\nA: 10π\nB: 12π\nC: 14π\nD: 16π"
},
{
... | [
"mulberry_images/geoqa_plus/2129.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194956 | [
{
"from": "user",
"value": "<image>Provided is a figure containing circle O with diameters AB and CD. The chords DF and BE are drawn to create arcs DF and BE of equal length. Given that angle B measures 50.0 degrees, what is the degree of angle D?\nChoices:\nA: 25°\nB: 40°\nC: 50°\nD: 60°"
},
{
"fro... | [
"mulberry_images/geoqa_plus/1695.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194957 | [
{
"from": "user",
"value": "<image>In the provided figure, where circle O has AB as its diameter and points C and D lie on the circle, angle BOC measures 110.0 degrees. If AD is parallel to OC, what is the measure of angle ABD?\nChoices:\nA: 20°\nB: 30°\nC: 40°\nD: 50°"
},
{
"from": "assistant",
... | [
"mulberry_images/geoqa_plus/1767.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194958 | [
{
"from": "user",
"value": "<image>Consider the figure showing a cone-shaped Christmas hat. The hat's bottom part has a radius of 8.0. If we cut along the generatrix AB, and the length of AB is 20.0, not including any seam or loss, what is the minimum surface area of cardboard needed to construct this parti... | [
"mulberry_images/geoqa_plus/2238.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194959 | [
{
"from": "user",
"value": "<image>Considering the figure provided, where AB is parallel to CD and both are parallel to EF, and angle ABE measures 70.0 degrees while angle DCE measures 144.0 degrees, what is the value of angle BEC?\nChoices:\nA: 34°\nB: 36°\nC: 44°\nD: 46°"
},
{
"from": "assistant",... | [
"mulberry_images/geoqa_plus/1568.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194960 | [
{
"from": "user",
"value": "<image>In the given figure depicting a measuring tool ABC, it is being used to measure the diameter of a small glass tube. The length of AB is 12.0 units, and AC is divided into 60.0 equal parts. If we assume that the port DE of the small glass tube is positioned exactly over the... | [
"mulberry_images/geoqa_plus/2361.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194961 | [
{
"from": "user",
"value": "<image>In the figure provided, circle O is shown with radii OA and OB. Point C is positioned on circle O. If angle AOB is 40.0 degrees and angle OCB is 50.0 degrees, what degree measure does angle OAC have?\nChoices:\nA: 20°\nB: 30°\nC: 40°\nD: 50°"
},
{
"from": "assistan... | [
"mulberry_images/geoqa_plus/1732.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194962 | [
{
"from": "user",
"value": "<image>If right triangle ABC is rotated once around the line AC, forming a cone, what is the surface area of the cone? The right triangle has angle BAC measuring 90 degrees, AB measuring 2.0 units, and BC measuring 5.0 units.\nChoices:\nA: 10π\nB: 12π\nC: 14π\nD: 16π"
},
{
... | [
"mulberry_images/geoqa_plus/2129.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194963 | [
{
"from": "user",
"value": "<image>When considering the figure that demonstrates triangle ABC, with angle B measuring 55.0 degrees and angle C measuring 63.0 degrees, and knowing that DE is parallel to AB, what is the measure of angle DEC?\nChoices:\nA: 63°\nB: 113°\nC: 55°\nD: 62°"
},
{
"from": "as... | [
"mulberry_images/geoqa_plus/5081.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194964 | [
{
"from": "user",
"value": "<image>Given that points A, B, and C are located on circle O and angle ACB is equal to 40.0 degrees, what is the degree measure of angle AOB?\nChoices:\nA: 40°\nB: 50°\nC: 80°\nD: 100°"
},
{
"from": "assistant",
"value": "<think> Okay, let me think about this problem.... | [
"mulberry_images/geoqa_plus/2223.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194965 | [
{
"from": "user",
"value": "<image>In the provided figure, the cone has a bottom surface radius of 3.0 and a height of 4.0. What is the lateral area of the cone?\nChoices:\nA: 10πcm^{2}\nB: 15πcm^{2}\nC: 20πcm^{2}\nD: 25πcm^{2}"
},
{
"from": "assistant",
"value": "<think> Okay, let's see. The pr... | [
"mulberry_images/geoqa_plus/2230.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194966 | [
{
"from": "user",
"value": "<image>In the provided figure, with the bottom radius OB measuring 6.0 and the height CO measuring 8.0, what is the central angle of the expanded figure of the cone's lateral surface?\nChoices:\nA: 120°\nB: 180°\nC: 216°\nD: 236°"
},
{
"from": "assistant",
"value": "<... | [
"mulberry_images/geoqa_plus/2130.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194967 | [
{
"from": "user",
"value": "<image>If the generatrix of the cone measures 10.0 and the diameter of the bottom circle is 12.0, what is the lateral area of the cone?\nChoices:\nA: 24π\nB: 30π\nC: 48π\nD: 60π"
},
{
"from": "assistant",
"value": "<think> Okay, let's see. The problem is asking for th... | [
"mulberry_images/geoqa_plus/2149.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194968 | [
{
"from": "user",
"value": "<image>In the given trapezoid ABCD, with AD parallel to BC and E and F as the midpoints of the diagonals BD and AC, respectively, if AD measures 6.0 and BC measures 18.0, what is the length of EF?\nChoices:\nA: 8cm\nB: 7cm\nC: 6cm\nD: 5cm"
},
{
"from": "assistant",
"v... | [
"mulberry_images/geoqa_plus/4969.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194969 | [
{
"from": "user",
"value": "<image>Suppose circles with a radius of 1.0 are created at each vertex of the quadrilateral ABCD in the provided figure. What is the sum of the areas of the shaded sectors?\nChoices:\nA: 2π\nB: π\nC: \\frac{2}{3}π\nD: \\frac{π}{2}"
},
{
"from": "assistant",
"value": "... | [
"mulberry_images/geoqa_plus/2004.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194970 | [
{
"from": "user",
"value": "<image>In the given diagram, circle O is depicted, with chord AB recording a measurement of 18.0 units. Moreover, M is recognized as the midpoint of AB, and as OM is found to measure 12.0 units, what is the value of the radius of circle O?\nChoices:\nA: 8\nB: 2\nC: 10\nD: 15"
}... | [
"mulberry_images/geoqa_plus/5122.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194971 | [
{
"from": "user",
"value": "<image>Point A and point D are located on circle O, where BC represents the diameter of the circle. If angle ADB is found to be 70.0 degrees, what is the measure of angle ABC?\nChoices:\nA: 20°\nB: 70°\nC: 30°\nD: 90°"
},
{
"from": "assistant",
"value": "<think> Okay,... | [
"mulberry_images/geoqa_plus/1788.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194972 | [
{
"from": "user",
"value": "<image>What is the lateral area of the conical Christmas hat shown in the figure, which has a generatrix length of 2.0 and a bottom radius of 1.0? \nChoices:\nA: 2\nB: π\nC: 2π\nD: 4π"
},
{
"from": "assistant",
"value": "<think> Okay, so I need to find the lateral are... | [
"mulberry_images/geoqa_plus/2190.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194973 | [
{
"from": "user",
"value": "<image>In the given diagram showcasing circle O, chords AB and AC intersect the circle and points M and N are the feet of the perpendiculars OM and ON drawn from M and N respectively. If MN measures 3.0 units, what is the measurement of BC?\nChoices:\nA: 4\nB: 5\nC: 6\nD: 7"
},... | [
"mulberry_images/geoqa_plus/5111.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194974 | [
{
"from": "user",
"value": "<image>In the provided figure, triangle ABC is displayed with angle ABC measuring 90 degrees and angle A measuring 50 degrees. Calculate the degree measurement of angle C.\nChoices:\nA: 50°\nB: 40°\nC: 30°\nD: 45°"
},
{
"from": "assistant",
"value": "<think> Okay, so ... | [
"mulberry_images/geoqa_plus/1925.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194975 | [
{
"from": "user",
"value": "<image>Based on the provided diagram, if the bottom radius of a cone is OB = 6.0 and the height is OC = 8.0, what is 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'... | [
"mulberry_images/geoqa_plus/2006.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194976 | [
{
"from": "user",
"value": "<image>In the provided figure, if angle 1 is given as equal to angle 2 and angle D is calculated to be 78.0 degrees, what is the value of angle BCD?\nChoices:\nA: 98°\nB: 62°\nC: 88°\nD: 102°"
},
{
"from": "assistant",
"value": "<think> Okay, let's see. The problem is... | [
"mulberry_images/geoqa_plus/1393.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194977 | [
{
"from": "user",
"value": "<image>The figure shows a conical chimney cap 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})\nD: 120... | [
"mulberry_images/geoqa_plus/2282.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194978 | [
{
"from": "user",
"value": "<image>If the radius of the bottom surface of a cone is 3.0 and the height is 4.0, what is the measure of the cone's lateral area?\nChoices:\nA: 12π\nB: 15π\nC: 24π\nD: 30π"
},
{
"from": "assistant",
"value": "<think> Okay, let me see. The problem is asking for the la... | [
"mulberry_images/geoqa_plus/2010.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194979 | [
{
"from": "user",
"value": "<image>In the provided diagram, circle O contains chord AB, with radius OC intersecting AB at point D perpendicularly. Given that OB is equal to 10.0 units and CD is equal to 2.0 units, what is the length of AB?\nChoices:\nA: 8\nB: 12\nC: 16\nD: 20"
},
{
"from": "assistan... | [
"mulberry_images/geoqa_plus/5124.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194980 | [
{
"from": "user",
"value": "<image>In the given situation where a sector with a radius of 9.0 and a central angle of 120.0 is employed to enclose the lateral surface of a cone (with the exclusion of the joints), what is the radius of the cone's bottom?\nChoices:\nA: 9\nB: 3\nC: 1\nD: 6"
},
{
"from":... | [
"mulberry_images/geoqa_plus/2037.png"
] | vision_r1_mulberry_sft_full |
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