id stringlengths 29 36 | conversations listlengths 1 48 | images listlengths 1 1 | source_dataset stringclasses 2
values |
|---|---|---|---|
vision_r1_mulberry_sft_full-193981 | [
{
"from": "user",
"value": "<image>Given the figure displaying quadrilateral ABCD, if the sum of angles B and D equals 140 degrees, what is the measure of angle C?\nChoices:\nA: 140°\nB: 120°\nC: 110°\nD: 100°"
},
{
"from": "assistant",
"value": "<think> Okay, let's see. The problem depicts ABCD... | [
"mulberry_images/geoqa_plus/10038.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-193982 | [
{
"from": "user",
"value": "<image>As depicted in the figure, the straight line AB runs parallel to CD, and the straight line EF intersects AB and CD at points E and F respectively. Moreover, the bisector of angle BEF intersects at point N. If angle 1 measures 63.0 degrees, then what is the measure of angle... | [
"mulberry_images/geoqa_plus/209.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-193983 | [
{
"from": "user",
"value": "<image>In the given diagram, there exists a parallelogram ABCD and a square CEFG. The point E lies on the line segment AD. If the angle ECD is equal to 35.0 degrees and the angle AEF is equal to 15.0 degrees, what is the measure of angle B?\nChoices:\nA: 50\nB: 55\nC: 70\nD: 75"
... | [
"mulberry_images/geoqa_plus/502.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-193984 | [
{
"from": "user",
"value": "<image>Suppose angle A in triangle ABC has a measurement of 40.0 degrees. If a right triangular plate DEF is positioned on the triangle in such a way that its legs DE and DF pass through points B and C respectively, what is the value of angle ABD added to angle ACD?\nChoices:\nA:... | [
"mulberry_images/geoqa_plus/841.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-193985 | [
{
"from": "user",
"value": "<image>If angle C in triangle ABC measures 90.0 degrees, with BC at 5.0 units and AB at 13.0 units, what is the sine value of angle B?\nChoices:\nA: \\frac{5}{13}\nB: \\frac{5}{12}\nC: \\frac{12}{13}\nD: \\frac{13}{12}"
},
{
"from": "assistant",
"value": "<think> Okay... | [
"mulberry_images/geoqa_plus/2588.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-193986 | [
{
"from": "user",
"value": "<image>In the provided figure, with AD as the midline of triangle ABC and AB measuring 5.0 units, while AC measures 3.0 units, what is the difference in perimeter between triangle ABD and triangle ACD?\nChoices:\nA: 6\nB: 3\nC: 2\nD: 不确定"
},
{
"from": "assistant",
"va... | [
"mulberry_images/geoqa_plus/5245.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-193987 | [
{
"from": "user",
"value": "<image>Provided in the figure is parallelogram ABCD. It is important to mention that AB and AD are not equal. The intersection of the diagonals AC and BD is point O, and the line segment OE is perpendicular to BD and intersects AD at point E. Given that the perimeter of triangle ... | [
"mulberry_images/geoqa_plus/9532.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-193988 | [
{
"from": "user",
"value": "<image>If point A is selected on the opposite bank and points B and C are chosen on this side of the river, such that AB is perpendicular to BC, and EC is perpendicular to BC, the measurements reveal that BD is 120.0, DC is 60.0, and EC is 50.0. What would be the approximate widt... | [
"mulberry_images/geoqa_plus/2310.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-193989 | [
{
"from": "user",
"value": "<image>As depicted in the figure, in triangle ABC where AB is equal to AC, BC measures 9.0 units, and point D is located on the side AB with BD equal to 5.0 units, if the line segment BD is translated in the direction of BC to obtain line segment EF, and the translation distance ... | [
"mulberry_images/geoqa_plus/5706.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-193990 | [
{
"from": "user",
"value": "<image>As shown in the diagram, angle AOB is a straight angle. angle AOC = 40°, and angle BOD = 26°. OM and ON are the bisectors of angle AOC and angle BOD respectively. Therefore, angle MON is equal to ().\nChoices:\nA: 66°\nB: 114°\nC: 147°\nD: 170°"
},
{
"from": "assis... | [
"mulberry_images/geoqa_plus/10945.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-193991 | [
{
"from": "user",
"value": "<image>Given the figure displaying parallelogram ABCD, where line EF runs parallel to line AB and intersects line AD at point E and line BD at point F, with the ratio DE:EA being 3:4 and the length of line EF equaling 6.0, what is the measurement of line segment CD?\nChoices:\nA:... | [
"mulberry_images/geoqa_plus/7438.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-193992 | [
{
"from": "user",
"value": "<image>As shown in the figure, in triangle ABC, AB = AC = 13.0, BC = 10.0, AD bisects angle BAC and intersects BC at point D, the perpendicular bisector of AD intersects AC at point E,. Connect DE, then the perimeter of triangle CDE is ()\nChoices:\nA: 23\nB: 26\nC: 18\nD: 15"
... | [
"mulberry_images/geoqa_plus/5701.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-193993 | [
{
"from": "user",
"value": "<image>If in the quadrilateral ABCD, AD is equal to BC and E, F, and G are the midpoints of AB, CD, and AC, and angle DAC equals 15.0 degrees while angle ACB equals 87.0 degrees, what is the measure of angle FEG?\nChoices:\nA: 39°\nB: 18°\nC: 72°\nD: 36°"
},
{
"from": "as... | [
"mulberry_images/geoqa_plus/5972.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-193994 | [
{
"from": "user",
"value": "<image>Given a figure showing parallelogram ABCD, where AB measures 6.0 units and AD measures 9.0 units, if the bisector of angle BAD intersects the extended line of DC at a point denoted as E, what is the measurement of CE?\nChoices:\nA: 2\nB: 3\nC: 4\nD: 2.5"
},
{
"from... | [
"mulberry_images/geoqa_plus/9370.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-193995 | [
{
"from": "user",
"value": "<image>Let's consider the parallelogram ABCD shown in the figure. With angle B measuring 80 degrees and AE acting as the angle bisector of angle BAD, intersecting BC at point E, and CF running parallel to AE while intersecting AD at point F, what is the degree measure of angle 1?... | [
"mulberry_images/geoqa_plus/9464.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-193996 | [
{
"from": "user",
"value": "<image>Circle O is depicted in the figure, and it contains an arc AB. The central angle ACB is associated with this arc. Along the secant line of circle O lies point P, and the midpoints of line segments PA and PB are labeled D and E respectively. If the radius of circle O measur... | [
"mulberry_images/geoqa_plus/3216.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-193997 | [
{
"from": "user",
"value": "<image>Given the figure with quadrilateral ABCD, where O is the intersection of its diagonals and E is the midpoint of side AB, line segment DE intersects line segment AC at point F. If the area of quadrilateral ABCD is 12.0, what is the area of triangle DOE?\nChoices:\nA: 1\nB: ... | [
"mulberry_images/geoqa_plus/9393.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-193998 | [
{
"from": "user",
"value": "<image>In the figure provided, parallelogram ABCD is shown, with point E lying on side AB and the lines CE and BD intersecting at point F. If the ratio of AE to BE is 2:1 and BF measures 2 units, what is the length, in units, of segment DF?\nChoices:\nA: 4\nB: 3\nC: 4\nD: 6"
},... | [
"mulberry_images/geoqa_plus/7256.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-193999 | [
{
"from": "user",
"value": "<image>Given that angle NAM is 30.0 degrees and point O lies on the edge AN, let's consider the scenario where circle O, with a radius of 2.0 units, intersects the edge AN at points D and E. If circle O is tangent to line segment AM, what is the length of AD? \nChoices:\nA: 4\nB:... | [
"mulberry_images/geoqa_plus/3954.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194000 | [
{
"from": "user",
"value": "<image>Consider a right triangle ABC, where angle ACB measures 90°. Let points G, E, and D be the midpoints of sides AB, BC, and CA, respectively. If DE + CG equals 7, then what is the length of CG? Represent the length of CG as 'x'.\nChoices:\nA: 3\nB: 3.5\nC: 4\nD: 5"
},
{
... | [
"mulberry_images/geoqa_plus/12139.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194001 | [
{
"from": "user",
"value": "<image>In triangle ABC, with AB = 8 and BC = 6, the perpendicular bisector of side AC intersects AB and AC at points M and N. Determine the perimeter of triangle BCM. Express the perimeter of triangle BCM as 'P'.\nChoices:\nA: 7\nB: 10\nC: 11\nD: 14"
},
{
"from": "assista... | [
"mulberry_images/geoqa_plus/12286.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194002 | [
{
"from": "user",
"value": "<image>Given that points A, B, C, and D are all on circle O, and OA is perpendicular to BC, if angle AOB measures 50 degrees, what is the degree measurement of angle ADC?\nChoices:\nA: 50°\nB: 40°\nC: 30°\nD: 25°"
},
{
"from": "assistant",
"value": "<think> Okay, let ... | [
"mulberry_images/geoqa_plus/3314.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194003 | [
{
"from": "user",
"value": "<image>How far apart are points A and C after the reflection of point A over line EF to point B, followed by the reflection of point B over line MN to point C, considering the intersection of lines MN and EF at point O, angle EON measuring 45.0 degrees, AO having a length of 2.0,... | [
"mulberry_images/geoqa_plus/5659.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194004 | [
{
"from": "user",
"value": "<image>Given an equilateral triangle ABC and its specifications including AC measuring 4.0 units, with points D, E, and F located on the edges AB, BC, and AC respectively. Additionally, AF measures 1.0 unit, FD is perpendicular to DE, and angle DFE equals 60.0 degrees, what is th... | [
"mulberry_images/geoqa_plus/7649.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194005 | [
{
"from": "user",
"value": "<image>Given AC as the cable of the pole with BC measuring 4.0 units and angle ACB measuring 60.0 degrees, what is the length of AB?\nChoices:\nA: 8米\nB: 4√{3}米\nC: 6米\nD: 2√{3}米"
},
{
"from": "assistant",
"value": "<think> Okay, let me try to figure this out. So ther... | [
"mulberry_images/geoqa_plus/8347.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194006 | [
{
"from": "user",
"value": "<image>If the figure provided represents trapezoid ABCD, with AD parallel to BC, AD measuring 3 units, AB measuring 5 units, and BC measuring 9 units, and the perpendicular bisector of CD intersects BC at point E, what is the total perimeter of quadrilateral ABED?\nChoices:\nA: 1... | [
"mulberry_images/geoqa_plus/12874.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194007 | [
{
"from": "user",
"value": "<image>In the given diagram, let circle O be tangential to the two sides AB and AD of square ABCD, and let DE be tangential to circle O at point E. If DE measures 6.0 units and AB measures 11.0 units, what is the radius of circle O? Represent the radius as 'r'.\nChoices:\nA: 5\nB... | [
"mulberry_images/geoqa_plus/4035.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194008 | [
{
"from": "user",
"value": "<image>In the figure provided, a student who stands 1.6 meters tall endeavors to determine the height of a flagpole. By positioning himself at point C, the student discovers that the shadow cast by the top of his head aligns perfectly with the shadow of the flagpole at point A. R... | [
"mulberry_images/geoqa_plus/2315.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194009 | [
{
"from": "user",
"value": "<image>As observed in the figure, the quadrilateral ABCD is represented, with the line segment AE forming a right angle with BC at point E, and the line segment AF forming a right angle with CD at point F. Furthermore, AE measures 3cm and AF measures 4cm. With the perimeter of AB... | [
"mulberry_images/geoqa_plus/12525.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194010 | [
{
"from": "user",
"value": "<image>Assuming the given figure with circle O and points A, B, and D, where angle A measures 20.0 degrees, BC is tangent to circle O at point B, and the extended line of OD intersects BC at point C, what is the size of angle OCB?\nChoices:\nA: 20°\nB: 40°\nC: 50°\nD: 80°"
},
... | [
"mulberry_images/geoqa_plus/3913.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194011 | [
{
"from": "user",
"value": "<image>In rectangle ABCD, AC and BD intersect at point O. M and N represent the midpoints of AB and OA, respectively. Given that MN measures 2 units, what is the length of AC?\nChoices:\nA: 2√{2}\nB: 4\nC: 4√{2}\nD: 8"
},
{
"from": "assistant",
"value": "<think> Okay,... | [
"mulberry_images/geoqa_plus/12941.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194012 | [
{
"from": "user",
"value": "<image>In the given figure, circle O has parallelogram ABCD inscribed within it, with vertices A, B, and D lying on the circle and vertex C lying on diameter BE. If angle E measures 36.0 degrees when segment AE is connected, what is the measure of angle ADC?\nChoices:\nA: 54°\nB:... | [
"mulberry_images/geoqa_plus/3015.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194013 | [
{
"from": "user",
"value": "<image>If pentagon ABCDE is symmetrical with respect to line l passing through point A, and angle DAE is 40.0 degrees while angle ADE is 60.0 degrees, what is the measure of angle B?\nChoices:\nA: 60°\nB: 40°\nC: 80°\nD: 100°"
},
{
"from": "assistant",
"value": "<thin... | [
"mulberry_images/geoqa_plus/5664.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194014 | [
{
"from": "user",
"value": "<image>Let triangle ABC be presented in the diagram, with angle ABC measuring 80.0 degrees and angle ACB measuring 60.0 degrees. Suppose BE and CF are the angular bisectors of triangle ABC, intersecting at point D. How large is angle CDE in degrees?\nChoices:\nA: 110°\nB: 70°\nC:... | [
"mulberry_images/geoqa_plus/132.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194015 | [
{
"from": "user",
"value": "<image>In the given figure, PA and PB are tangents to circle O at points A and B, respectively. Point C is positioned on circle O, and angle ACB measures 52°. Determine the measure of angle APB.\nChoices:\nA: 104°\nB: 76°\nC: 128°\nD: 63°"
},
{
"from": "assistant",
"v... | [
"mulberry_images/geoqa_plus/10245.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194016 | [
{
"from": "user",
"value": "<image>Consider the given diagram of quadrilateral ABCD, where AB has a length of 4.0 and BC has a length of 6.0. Additionally, AB is perpendicular to BC and BC is perpendicular to CD. The midpoint of AD is denoted as point E, and there is a point F on the line segment BE where F... | [
"mulberry_images/geoqa_plus/7430.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194017 | [
{
"from": "user",
"value": "<image>Let's suppose there is a figure in which angle B is 50.0 degrees, and BC is perpendicular to AE while CD is parallel to AB. Find the degree measure of angle 1 in this scenario.\nChoices:\nA: 40°\nB: 45°\nC: 50°\nD: 55°"
},
{
"from": "assistant",
"value": "<thin... | [
"mulberry_images/geoqa_plus/498.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194018 | [
{
"from": "user",
"value": "<image>As shown in the figure, in the rectangle ABCD, AB = 2.0, BC = 3.0, draw a circle with A and D as the center and 1.0 as the radius respectively, E and F are the moving points on circle A and circle D respectively, and P is the move on BC Point, then the minimum value of PE ... | [
"mulberry_images/geoqa_plus/5922.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194019 | [
{
"from": "user",
"value": "<image>Parallelogram ABCD is shown in the diagram, with its diagonals intersecting at point O. It is known that AD and CD have different lengths, and that OM is perpendicular to AC, intersecting AD at point M. Given the perimeter of triangle CDM is 5, what is the perimeter of par... | [
"mulberry_images/geoqa_plus/13099.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194020 | [
{
"from": "user",
"value": "<image>As shown in the diagram, AD is a tangent to circle O with point A as the point of tangency. Line DO intersects circle O at point C, and point B is on circle O. Connect lines AB and CB. If angle D = 36°, then the degree measure of angle ABC is ().\nChoices:\nA: 36°\nB: 34°\... | [
"mulberry_images/geoqa_plus/10347.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194021 | [
{
"from": "user",
"value": "<image>Consider parallelogram ABCD, where AC and BD intersect at point O. A straight line passing through O intersects opposite edges at points E and F. If the total area of the shaded part in the figure is 2.0, what is the area of parallelogram ABCD?\nChoices:\nA: 12\nB: 8\nC: 6... | [
"mulberry_images/geoqa_plus/9428.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194022 | [
{
"from": "user",
"value": "<image>In the provided figure, circle O is shown with the radius OA perpendicular to the chord BC. If angle AOB is 50.0 degrees and point D is located on the circle, what is the degree measure of angle ADC?\nChoices:\nA: 50°\nB: 40°\nC: 30°\nD: 25°"
},
{
"from": "assistan... | [
"mulberry_images/geoqa_plus/9683.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194023 | [
{
"from": "user",
"value": "<image>In the given triangle ABC, if the measure of angle AED is the same as angle B, and the lengths of DE, AB, and AE are 6.0, 10.0, and 8.0, what is the length of BC?\nChoices:\nA: \\frac{15}{4}\nB: 7\nC: \\frac{15}{2}\nD: \\frac{24}{5}"
},
{
"from": "assistant",
"... | [
"mulberry_images/geoqa_plus/7783.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194024 | [
{
"from": "user",
"value": "<image>In the figure provided, parallelogram ABCD has a perimeter of 20.0 units. Point O represents the intersection of lines AC and BD. At point E, line OE is perpendicular to line AC, and line AC intersects line AD. Find the perimeter of triangle CDE.\nChoices:\nA: 6cm\nB: 8cm\... | [
"mulberry_images/geoqa_plus/9352.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194025 | [
{
"from": "user",
"value": "<image>In the figure provided, the straight line l intersects the circle O at two points A and B, and forms a perpendicular intersection with the radius OC. The foot of the perpendicular is labeled as H. If AB equals 16.0 cm and OB equals 10.0 cm, what is the value of CH?\nChoice... | [
"mulberry_images/geoqa_plus/5201.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194026 | [
{
"from": "user",
"value": "<image>In the given figure, triangle ABC is circumscribed in circle O. If angle BAC measures 120.0 degrees, and the lengths of AB and AC are both 4.0 units, find the length of the diameter BD of circle O.\nChoices:\nA: 4\nB: 6\nC: 8\nD: 12"
},
{
"from": "assistant",
"... | [
"mulberry_images/geoqa_plus/8508.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194027 | [
{
"from": "user",
"value": "<image>In the given diagram, angle ABC and angle ACD are both 90 degrees. The length of BC is 2 units and AC is equal to CD. Calculate the area of triangle BCD.\nChoices:\nA: 2\nB: 4\nC: √{6}\nD: 6"
},
{
"from": "assistant",
"value": "<think> Okay, let's see. There ar... | [
"mulberry_images/geoqa_plus/11816.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194028 | [
{
"from": "user",
"value": "<image>Given the presence of triangle ABC in the illustrated diagram, where point I corresponds to the incenter and the lengths of sides AB, AC, and BC are measured at 4cm, 3cm, and 2cm respectively, what is the total perimeter of the shaded region in the diagram once angle ACB h... | [
"mulberry_images/geoqa_plus/12655.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194029 | [
{
"from": "user",
"value": "<image>In the figure provided, which illustrates parallelogram ABCD, point C marks the intersection of line segments CE and AB. The line segment CE is perpendicular to AB, with E as the foot of the perpendicular. If angle BCE is measured at 42.0 degrees, what is the degree measur... | [
"mulberry_images/geoqa_plus/9227.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194030 | [
{
"from": "user",
"value": "<image>With reference to the diagram of triangle ABC and circumscribed circle O, if angle ABO is measured at 20 degrees and angle OAC is measured at 40 degrees, what is the measure of angle OBC?\nChoices:\nA: 30°\nB: 40°\nC: 60°\nD: 120°"
},
{
"from": "assistant",
"va... | [
"mulberry_images/geoqa_plus/3652.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194031 | [
{
"from": "user",
"value": "<image>Consider the given figure where PA and PB are tangents to circle O at points A and B respectively. Angle ACB is known to be 65.0 degrees. What is the measure of angle APB in this case?\nChoices:\nA: 65°\nB: 50°\nC: 45°\nD: 40°"
},
{
"from": "assistant",
"value"... | [
"mulberry_images/geoqa_plus/3905.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194032 | [
{
"from": "user",
"value": "<image>In the given diagram, triangle ABC is shown with DE parallel to AB and also parallel to FG, while the area of triangle ABC is 32.0 and the area of triangle CDE is 2.0. Given the ratio of the distance from FG to DE and AB being 1.0:2.0, what is the area S of triangle CFG?\n... | [
"mulberry_images/geoqa_plus/8014.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194033 | [
{
"from": "user",
"value": "<image>In the given figure, let's denote the central angle BOC as variable x where x = 50.0 degrees. If the radius OC of circle O is perpendicular to chord AB, and D is a point on the major arc AB (not coincident with vertices A and B), what is the measure of angle ADC, expressed... | [
"mulberry_images/geoqa_plus/1133.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194034 | [
{
"from": "user",
"value": "<image>As shown in the figure, AB is the diameter of a semicircle, CD is a chord of the semicircle, and CD is parallel to AB. Additionally, angle ACD = 26°. Therefore, angle B is equal to ().\nChoices:\nA: 26°\nB: 36°\nC: 64°\nD: 74°"
},
{
"from": "assistant",
"value"... | [
"mulberry_images/geoqa_plus/10283.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194035 | [
{
"from": "user",
"value": "<image>Given the figure where AB parallels CF and E is the midpoint of DF, what is the length of BD if AB has a measure of 8.0 cm and CF has a measure of 5.0 cm?\nChoices:\nA: 2㎝\nB: 3㎝\nC: 4㎝\nD: 1㎝"
},
{
"from": "assistant",
"value": "<think> Okay, so I need to find... | [
"mulberry_images/geoqa_plus/732.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194036 | [
{
"from": "user",
"value": "<image>As shown in the diagram, AB is the diameter of circle O, and C, D are two points on the circle. It is given that angle DCB = 30°. Thus, angle AOD = ().\nChoices:\nA: 125°\nB: 155°\nC: 60°\nD: 120°"
},
{
"from": "assistant",
"value": "<think> Okay, let's see. Th... | [
"mulberry_images/geoqa_plus/10218.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194037 | [
{
"from": "user",
"value": "<image>In the given diagram, line a and line b intersect at point O, and the measure of angle 1 is represented by the variable 'x' (x = 110°). What is the measure of angle 2, expressed as 'y' in terms of 'x'?\nChoices:\nA: 70°\nB: 90°\nC: 110°\nD: 130°"
},
{
"from": "assi... | [
"mulberry_images/geoqa_plus/10859.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194038 | [
{
"from": "user",
"value": "<image>Given that points E and F are the midpoints of BD and CE respectively in the accompanying figure, and the area of triangle AEF is 3 square units, what is the area of triangle ABC?\nChoices:\nA: 9\nB: 10\nC: 11\nD: 12"
},
{
"from": "assistant",
"value": "<think>... | [
"mulberry_images/geoqa_plus/12025.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194039 | [
{
"from": "user",
"value": "<image>In the diagram provided, where circle O is inscribed in quadrilateral ABCD with AB acting as the diameter, if angle BCD is 130 degrees and the tangent PD intersects the line AB at point P, what is the measure of angle ADP?\nChoices:\nA: 40°\nB: 45°\nC: 50°\nD: 65°"
},
... | [
"mulberry_images/geoqa_plus/8973.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194040 | [
{
"from": "user",
"value": "<image>In the given figure, triangle ABC is shown with angle bisectors AD and BE intersecting at point O. If angle BOD measures 66.0 degrees, what is the degree measure of angle ACB?\nChoices:\nA: 33°\nB: 28°\nC: 52°\nD: 48°"
},
{
"from": "assistant",
"value": "<think... | [
"mulberry_images/geoqa_plus/4939.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194041 | [
{
"from": "user",
"value": "<image>In the parallelogram ABCD, where CE is the bisector of angle DCB, intersecting AB at E, and DB intersects CE at O, if AB is 6.0 and BC is 4.0, what is the fractional value of OB divided by DB?\nChoices:\nA: \\frac{1}{3}\nB: \\frac{2}{5}\nC: \\frac{3}{7}\nD: \\frac{2}{3}"
... | [
"mulberry_images/geoqa_plus/7985.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194042 | [
{
"from": "user",
"value": "<image>Considering the provided diagram, where AB represents a chord of circle O (without being the diameter), point A is the center, and AB length is the radius used to draw an intersecting arc with circle O at point C, what line segments should be connected to form AC, BC, OB, ... | [
"mulberry_images/geoqa_plus/3230.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194043 | [
{
"from": "user",
"value": "<image>If an aircraft detects the target C on the ground plane directly below it in the air A, and the depression angle of the ground plane command station B from the aircraft is α = 30.0, what is the distance between the aircraft A and the command station B when the flying heigh... | [
"mulberry_images/geoqa_plus/6829.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194044 | [
{
"from": "user",
"value": "<image>In the figure, a rectangle ABCD is shown, where AB measures 2.0 units and BC measures 3.0 units. If AE divides angle BAD into two equal parts and EF is perpendicular to AE, how long is AF?\nChoices:\nA: 3√{2}\nB: 4\nC: 2√{5}\nD: √{10}"
},
{
"from": "assistant",
... | [
"mulberry_images/geoqa_plus/9090.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194045 | [
{
"from": "user",
"value": "<image>In the figure provided, a ladder AB is depicted as leaning against a wall. The distance between the foot of the ladder, represented by point B, and the wall is 1.4 units. Point D, situated on the ladder, is at a distance of 1.2 units from the wall, with BD measuring 0.5 un... | [
"mulberry_images/geoqa_plus/743.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194046 | [
{
"from": "user",
"value": "<image>In the figure provided, if BD is the angle bisector of triangle ABC, and angle DBA measures 30 degrees while angle ADB measures 80 degrees, what is the degree of angle C?\nChoices:\nA: 30°\nB: 40°\nC: 50°\nD: 60°"
},
{
"from": "assistant",
"value": "<think> Oka... | [
"mulberry_images/geoqa_plus/10066.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194047 | [
{
"from": "user",
"value": "<image>If we have a right triangle ABC, where angle ACB is 90.0 degrees, and CD is perpendicular to AB at point D, and AC measures 4.0 while BC measures 3.0, what is the sine of angle ACD?\nChoices:\nA: \\frac{4}{3}\nB: \\frac{3}{4}\nC: \\frac{4}{5}\nD: \\frac{3}{5}"
},
{
... | [
"mulberry_images/geoqa_plus/7132.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194048 | [
{
"from": "user",
"value": "<image>Calculate the length of BC if AB acts as the diameter of circle O, angle ADC measures 30.0 degrees, and OA measures 2.0 units.\nChoices:\nA: 2\nB: 4\nC: 2√{3}\nD: √{3}"
},
{
"from": "assistant",
"value": "<think> Okay, let's see. The problem is about a circle w... | [
"mulberry_images/geoqa_plus/8664.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194049 | [
{
"from": "user",
"value": "<image>If AB is the chord of circle O and CD is tangent to circle O at point B, what is the degree measure of angle OAB if angle ABC is 140.0 degrees?\nChoices:\nA: 40°\nB: 45°\nC: 50°\nD: 55°"
},
{
"from": "assistant",
"value": "<think> Okay, let's see. We have a cir... | [
"mulberry_images/geoqa_plus/3972.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194050 | [
{
"from": "user",
"value": "<image>In the given figure, points A, B, and C lie on circle O. If the measure of angle A is 66.0 degrees, what is the degree of angle OCB? Express the measure of angle OCB as 'x'.\nChoices:\nA: 48°\nB: 33°\nC: 28°\nD: 24°"
},
{
"from": "assistant",
"value": "<think> ... | [
"mulberry_images/geoqa_plus/1105.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194051 | [
{
"from": "user",
"value": "<image>In the provided figure, circle O is shown with diameter AB perpendicular to chord CD. The point of intersection of diameter AB and chord CD is marked as E. If angle A measures 15.0 degrees and the radius of circle O is 2.0, what is the length of chord CD?\nChoices:\nA: 2\n... | [
"mulberry_images/geoqa_plus/3271.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194052 | [
{
"from": "user",
"value": "<image>In the provided figure depicting the arrangement of triangle plates, if angle BAC and angle ADE are both 90 degrees, angle E is 45 degrees, angle C is 30 degrees, the midpoint D is located on line segment BC, and AE is parallel to BC, how many degrees does angle DAC measur... | [
"mulberry_images/geoqa_plus/1514.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194053 | [
{
"from": "user",
"value": "<image>In the provided figure, where trapezoid ABCD is shown with AD parallel to BC and measuring 3 units, AB measuring 5 units, BC measuring 9 units, and the perpendicular bisector of CD intersecting BC at point E, what is the perimeter of quadrilateral ABED?\nChoices:\nA: 17\nB... | [
"mulberry_images/geoqa_plus/12874.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194054 | [
{
"from": "user",
"value": "<image>If in the figure, AB is parallel to DF, AC is perpendicular to CE at C, and the intersection of BC and DF is at point E, what is the measure of angle CEF given that angle A equals 20.0 degrees?\nChoices:\nA: 110°\nB: 100°\nC: 80°\nD: 70°"
},
{
"from": "assistant",
... | [
"mulberry_images/geoqa_plus/5382.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194055 | [
{
"from": "user",
"value": "<image>In triangle ABC, as shown in the figure, angle ABC is known to be 70.0 degrees and angle ACB is known to be 60.0 degrees. It is given that line segment BE is perpendicular to line segment AC at point E, and line segment CF is perpendicular to line segment AB at point F. Po... | [
"mulberry_images/geoqa_plus/757.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194056 | [
{
"from": "user",
"value": "<image>As depicted in the figure, circle O is represented with AB as the diameter. A chord, CD, is also present. Joining AC and AD, if the angle BAD is determined to be 27.0 degrees, what degree measure does angle ACD have?\nChoices:\nA: 73°\nB: 63°\nC: 54°\nD: 53°"
},
{
... | [
"mulberry_images/geoqa_plus/1859.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194057 | [
{
"from": "user",
"value": "<image>As shown in the figure, the quadrilateral ABCD is the inscribed quadrilateral of circle O, angle ABC = 100.0, then angle ADC = ()\nChoices:\nA: 70°\nB: 80°\nC: 90°\nD: 100°"
},
{
"from": "assistant",
"value": "<think> Okay, so there's a circle with quadrilatera... | [
"mulberry_images/geoqa_plus/3578.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194058 | [
{
"from": "user",
"value": "<image>Given that the quadrilateral ABCD is inscribed in circle O, and angle BOD measures 110.0 degrees, what is the degree measure of angle BCD?\nChoices:\nA: 55°\nB: 70°\nC: 110°\nD: 125°"
},
{
"from": "assistant",
"value": "<think> Okay, so I need to find the measu... | [
"mulberry_images/geoqa_plus/3449.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194059 | [
{
"from": "user",
"value": "<image>In the diagram showing triangle ABC, with D and E as the midpoints of sides AB and AC, and connected by DE, if angle B is 50 degrees and angle A is 60 degrees, what is the degree measure of angle AED?\nChoices:\nA: 50°\nB: 60°\nC: 70°\nD: 80°"
},
{
"from": "assista... | [
"mulberry_images/geoqa_plus/10023.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194060 | [
{
"from": "user",
"value": "<image>Given triangle ABC with D and E as points on sides AB and BC, respectively, such that AD is twice the length of BD and BE is equal to CE. If the area of triangle ABC is 12, what is the value of the difference S1 - S2, where S1 represents the area of triangle ADF and S2 rep... | [
"mulberry_images/geoqa_plus/12009.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194061 | [
{
"from": "user",
"value": "<image>When considering circle O with BD as the diameter and an inscribed angle CBD measuring 20.0, what is the measure of angle A on the circumference?\nChoices:\nA: 20°\nB: 70°\nC: 40°\nD: 50°"
},
{
"from": "assistant",
"value": "<think> Okay, so I need to find the ... | [
"mulberry_images/geoqa_plus/8605.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194062 | [
{
"from": "user",
"value": "<image>If CD is perpendicular to OA, and CE is perpendicular to OB in circle O, with point C moving clockwise on the arc AB, and GH on CE and CD where CG=frac {1.0}{3.0}CE, CH=frac {1.0}{3.0}CD, then what is the length of GH with a known radius of 6.0?\nChoices:\nA: 3\nB: 2\nC: 1... | [
"mulberry_images/geoqa_plus/7588.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194063 | [
{
"from": "user",
"value": "<image>In the diagram provided, let AB denote the diameter of circle O and AC represent the tangent to circle O. Connect OC, intersecting circle O at point D, and join BD. Given that angle C equals 40.0, determine the measure of angle ABD in terms of a variable.\nChoices:\nA: 30°... | [
"mulberry_images/geoqa_plus/4351.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194064 | [
{
"from": "user",
"value": "<image>What is the measure of angle ACB if points A, B, and C are all on circle O, and the angle AOB measures 72 degrees according to the given figure?\nChoices:\nA: 54°\nB: 36°\nC: 28°\nD: 18°"
},
{
"from": "assistant",
"value": "<think> Okay, so there's this circle ... | [
"mulberry_images/geoqa_plus/10370.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194065 | [
{
"from": "user",
"value": "<image>A diagram illustrates a beam of parallel light entering a sheet that is parallel to the opposite side. If the angle (angle 1) created between the light ray and the lower right side of the sheet is 110°, what is the size of the angle (angle 2) formed between the light ray a... | [
"mulberry_images/geoqa_plus/10538.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194066 | [
{
"from": "user",
"value": "<image>What is the measure of angle DEF in triangle ABC, where angle B is 70 degrees and angle C is 50 degrees, and points D, E, and F are the midpoints of sides AB, BC, and CA respectively?\nChoices:\nA: 50°\nB: 60°\nC: 70°\nD: 65°"
},
{
"from": "assistant",
"value":... | [
"mulberry_images/geoqa_plus/10056.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194067 | [
{
"from": "user",
"value": "<image>In the figure, AB is parallel to CD and AD equally divides angle BAC. If angle CDA measures 70 degrees, what is the degree of angle CAD?\nChoices:\nA: 40°\nB: 50°\nC: .60°\nD: 70°"
},
{
"from": "assistant",
"value": "<think> Okay, let's see. So, the problem ill... | [
"mulberry_images/geoqa_plus/1047.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194068 | [
{
"from": "user",
"value": "<image>As indicated in the diagram, with AB as the diameter of circle O and points C and D situated on the circle, if angle AOC is 126°, what is the measure of angle CDB?\nChoices:\nA: 54°\nB: 64°\nC: 27°\nD: 37°"
},
{
"from": "assistant",
"value": "<think> Okay, let'... | [
"mulberry_images/geoqa_plus/10317.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194069 | [
{
"from": "user",
"value": "<image>In the given diagram where points A, B, and C are positioned on circle O and angle ABO measures 36 degrees, what is the degree measure of angle ACB?\nChoices:\nA: 54°\nB: 27°\nC: 36°\nD: 108°"
},
{
"from": "assistant",
"value": "<think> Okay, let's see. There's... | [
"mulberry_images/geoqa_plus/10289.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194070 | [
{
"from": "user",
"value": "<image>In the provided figure, circle O has AB as its diameter, and points C and D are situated on opposite sides of AB. Connecting OC, CD, and DA forms line segments. If angle BOC is 130 degrees, what is the measure of angle D?\nChoices:\nA: 15°\nB: 25°\nC: 35°\nD: 50°"
},
{... | [
"mulberry_images/geoqa_plus/10144.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194071 | [
{
"from": "user",
"value": "<image>When points A, B, and C are all positioned on circle O, and the angle ACB measures 36 degrees, what is the degree measurement of angle AOB?\nChoices:\nA: 18°\nB: 30°\nC: 36°\nD: 72°"
},
{
"from": "assistant",
"value": "<think> Okay, so the problem is about a ci... | [
"mulberry_images/geoqa_plus/10101.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194072 | [
{
"from": "user",
"value": "<image>What is the measure of angle ACB if angle OAB is known to be 25°, and circle O is the circumcircle of triangle ABC as shown in the diagram?\nChoices:\nA: 55°\nB: 65°\nC: 50°\nD: 60°"
},
{
"from": "assistant",
"value": "<think> Okay, let's try to figure this out... | [
"mulberry_images/geoqa_plus/10173.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194073 | [
{
"from": "user",
"value": "<image>Given that circle O is the circumcircle of triangle ABC with angle A equal to 50 degrees, and E being the midpoint of side BC, what is the degree measurement of angle CBD when extending OE to intersect circle O at D and connecting BD?\nChoices:\nA: 20°\nB: 21°\nC: 23°\nD: ... | [
"mulberry_images/geoqa_plus/10225.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194074 | [
{
"from": "user",
"value": "<image>With the information that angle BOC equals 130 degrees and points A, B, and C are positioned on circle O, what is the degree measurement of angle A?\nChoices:\nA: 65°\nB: 60°\nC: 55°\nD: 50°"
},
{
"from": "assistant",
"value": "<think> Okay, let's see. There's ... | [
"mulberry_images/geoqa_plus/10326.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194075 | [
{
"from": "user",
"value": "<image>When PA is a tangent to circle O at point A, and the extension of PO intersects circle O at point C, and angle P is 40 degrees, what is the measure of angle CQA as point Q moves on line AC? \nChoices:\nA: 115°\nB: 110°\nC: 105°\nD: 100°"
},
{
"from": "assistant",
... | [
"mulberry_images/geoqa_plus/10147.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194076 | [
{
"from": "user",
"value": "<image>In the given diagram, lines AB and CD are parallel. With angle C measuring 80° and angle ACD measuring 60°, what is the degree measure of angle BAD?\nChoices:\nA: 60°\nB: 50°\nC: 45°\nD: 40°"
},
{
"from": "assistant",
"value": "<think> Okay, let's try to figure... | [
"mulberry_images/geoqa_plus/10778.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194077 | [
{
"from": "user",
"value": "<image>Triangle ABC has point O as its circumcenter, with OB being a line segment. If angle OBC measures 28 degrees, what is the value of angle A?\nChoices:\nA: 28°\nB: 52°\nC: 56°\nD: 62°"
},
{
"from": "assistant",
"value": "<think> Okay, let me try to work through t... | [
"mulberry_images/geoqa_plus/10546.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194078 | [
{
"from": "user",
"value": "<image>In the given diagram, let's denote the length of DE as variable x (x = 2), and the length of AD as variable y. If DE is parallel to BC, AD is equal to 2 times DB, and DE = 2, what is the length of BC, denoted as variable z in terms of x and y?\nChoices:\nA: 6\nB: 5\nC: 4\n... | [
"mulberry_images/geoqa_plus/12241.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194079 | [
{
"from": "user",
"value": "<image>What is the angle measure of DEF if triangle ABC has angle B equal to 70 degrees and angle C equal to 50 degrees, and points D, E, and F are the midpoints of sides AB, BC, and CA respectively?\nChoices:\nA: 50°\nB: 60°\nC: 70°\nD: 65°"
},
{
"from": "assistant",
... | [
"mulberry_images/geoqa_plus/10056.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194080 | [
{
"from": "user",
"value": "<image>With reference to the given diagram, which illustrates points A, B, and C lying on circle O, if angle C is 54°, what is the degree measurement of angle AOB? \nChoices:\nA: 27°\nB: 36°\nC: 54°\nD: 108°"
},
{
"from": "assistant",
"value": "<think> Okay, let's see... | [
"mulberry_images/geoqa_plus/10643.png"
] | vision_r1_mulberry_sft_full |
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