id stringlengths 29 36 | conversations listlengths 1 48 | images listlengths 1 1 | source_dataset stringclasses 2
values |
|---|---|---|---|
vision_r1_mulberry_sft_full-193881 | [
{
"from": "user",
"value": "<image>If the line AB serves as the diameter of circle O, with the tangent line PA intersecting circle O at point A, and forming an intersection with PO at point C, and ultimately connecting to point B, then what is the degree of angle ABC if angle P measures 40.0?\nChoices:\nA: ... | [
"mulberry_images/geoqa_plus/4181.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-193882 | [
{
"from": "user",
"value": "<image>In the given figure, triangle ABC is shown, with midpoints D, E, and F on sides BC, AC, and AB respectively, and AH perpendicular to BC at H, FD measures 8. What is the length of HE?\nChoices:\nA: 20\nB: 16\nC: 12\nD: 8"
},
{
"from": "assistant",
"value": "<thi... | [
"mulberry_images/geoqa_plus/13032.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-193883 | [
{
"from": "user",
"value": "<image>In the figure showing triangle ABC, if angle AED is equivalent to angle B, and the measurements of DE, AB, and AE are 6.0, 10.0, and 8.0, then 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-193884 | [
{
"from": "user",
"value": "<image>In the figure, triangle ABC is shown with point E as the midpoint of BC, and AD is the bisector of angle BAC. If EF is parallel to AD and AB measures 7.0 while AC measures 11.0, what is the length of FC?\nChoices:\nA: 7\nB: 8\nC: 9\nD: 10"
},
{
"from": "assistant",... | [
"mulberry_images/geoqa_plus/7976.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-193885 | [
{
"from": "user",
"value": "<image>Consider the figure with point P inside parallelogram ABCD. Given that the area of triangle PAB is 7.0 and the area of triangle PAD is 4.0, what is the area of triangle PAC?\nChoices:\nA: 4\nB: 3.5\nC: 3\nD: 无法确定"
},
{
"from": "assistant",
"value": "<think> Oka... | [
"mulberry_images/geoqa_plus/9544.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-193886 | [
{
"from": "user",
"value": "<image>When quadrilateral ABCD is given with angle A measuring 110 degrees and angle B measuring 85 degrees, and triangle BMN is folded along MN to create triangle FMN with MF parallel to AD and FN parallel to DC, what is the measure of angle C?\nChoices:\nA: 70°\nB: 80°\nC: 90°\... | [
"mulberry_images/geoqa_plus/4923.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-193887 | [
{
"from": "user",
"value": "<image>How long should the fence be to enclose the quadrilateral EFGH field within the open space shaped like an isosceles trapezoid ABCD, with E, F, G, and H being the midpoints of each side, and a diagonal AC measuring 10.0?\nChoices:\nA: 40米\nB: 30米\nC: 20米\nD: 10米"
},
{
... | [
"mulberry_images/geoqa_plus/8.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-193888 | [
{
"from": "user",
"value": "<image>Let's denote angle A in the parallelogram ABCD as variable u, where u = 50.0 degrees. What is the degree measure of angle C, expressed as variable v in relation to u?\nChoices:\nA: 40°\nB: 50°\nC: 130°\nD: 150°"
},
{
"from": "assistant",
"value": "<think> Okay,... | [
"mulberry_images/geoqa_plus/9247.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-193889 | [
{
"from": "user",
"value": "<image>In triangle ABC, where AB = 8.0, AC = 5.0, and BC = 7.0, if AD is the bisector of the exterior angle of triangle ABC, CD is perpendicular to AD at point D, and E is the midpoint of BC shown in the figure, what is the length of DE?\nChoices:\nA: 7\nB: 6.5\nC: 6\nD: 5.5"
}... | [
"mulberry_images/geoqa_plus/4967.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-193890 | [
{
"from": "user",
"value": "<image>In diamond ABCD, shown in the figure, where the point O is the intersection of diagonals AC and BD, and with BE being equal to CE, AC measuring 6.0, and BD measuring 8.0, what is the length of segment OE?\nChoices:\nA: 2cm\nB: 3cm\nC: 4cm\nD: 2.5cm"
},
{
"from": "a... | [
"mulberry_images/geoqa_plus/9129.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-193891 | [
{
"from": "user",
"value": "<image>Given that in triangle ABC, segment DE is parallel to segment BC, the ratio of AE to EC is 4:5, and the length of DE is 1, what is the measure of segment BC?\nChoices:\nA: \\frac{5}{4}\nB: \\frac{3}{2}\nC: \\frac{9}{4}\nD: \\frac{13}{4}"
},
{
"from": "assistant",
... | [
"mulberry_images/geoqa_plus/7200.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-193892 | [
{
"from": "user",
"value": "<image>If we have an equilateral triangle ABC with an edge length of 3.0 units and point P is located on BC such that BP measures 1.0 unit, point D lies on AC. Throughout this triangle, angle APD is observed at 60.0 degrees. In light of these facts, what is the length of CD?\nCho... | [
"mulberry_images/geoqa_plus/7404.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-193893 | [
{
"from": "user",
"value": "<image>Given that AD is the angular bisector of triangle ABC and DE is parallel to AB intersecting AC at E, with AE/EC = 3/5, what is the ratio of AC to AB in the figure?\nChoices:\nA: \\frac{3}{5}\nB: \\frac{3}{2}\nC: \\frac{8}{5}\nD: \\frac{5}{3}"
},
{
"from": "assistan... | [
"mulberry_images/geoqa_plus/4639.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-193894 | [
{
"from": "user",
"value": "<image>If angle MON measures 90.0 degrees and points A and B move on the radial lines OM and ON respectively, what is the degree measure of angle C if BE bisects angle NBA and the reverse extended line of BE intersects the bisector of angle BAO at point C?\nChoices:\nA: 30°\nB: 4... | [
"mulberry_images/geoqa_plus/285.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-193895 | [
{
"from": "user",
"value": "<image>Given the figure provided, with AB acting as the diameter of circle O, AC functioning as a chord, OD being the perpendicular drawn from point D to AC, and OD measured at 1.0, what is the length of BC?\nChoices:\nA: 3cm\nB: 2cm\nC: 1.5cm\nD: 4cm"
},
{
"from": "assis... | [
"mulberry_images/geoqa_plus/8926.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-193896 | [
{
"from": "user",
"value": "<image>If triangle ABC has angle C equal to 90.0 degrees, angle A equal to 15.0 degrees, and angle DBC equal to 60.0 degrees, and with BC measuring 1.0 unit, then what would be the length of AD in this situation, as shown in the figure? \nChoices:\nA: 1.5\nB: 2\nC: 3\nD: 4"
},
... | [
"mulberry_images/geoqa_plus/5893.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-193897 | [
{
"from": "user",
"value": "<image>Given that triangle ABC is congruent to triangle DEF in the figure, with corresponding sides DF and AC, and FE and CB, and angle A measures 100.0 degrees and angle F measures 47.0 degrees, determine the measure of angle DEF.\nChoices:\nA: 100°\nB: 53°\nC: 47°\nD: 33°"
},... | [
"mulberry_images/geoqa_plus/718.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-193898 | [
{
"from": "user",
"value": "<image>Given the information that CE bisects angle DCB in parallelogram ABCD, and it intersects AB at E, while DB and CE intersect at O, and AB measures 6.0 and BC measures 4.0, what is the value of OB divided by DB?\nChoices:\nA: \\frac{1}{3}\nB: \\frac{2}{5}\nC: \\frac{3}{7}\nD... | [
"mulberry_images/geoqa_plus/7985.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-193899 | [
{
"from": "user",
"value": "<image>In the given diagram, let OA be the intersection point of the straight line EF with point A as the midpoint of segment EF, and let OE and OF be the connections of point A with O. If point A lies on the major arc CD and the angle E is measured as 40.0 units, what is the mea... | [
"mulberry_images/geoqa_plus/3959.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-193900 | [
{
"from": "user",
"value": "<image>In the diagram, circle O is intersected by chords AB and AC. A tangent drawn from point B intersects the extended line of AC at point D, with point E denoting the midpoint of arc AC. If angle EAB is 65.0 degrees, what is the measure of angle D after connecting AE?\nChoices... | [
"mulberry_images/geoqa_plus/4084.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-193901 | [
{
"from": "user",
"value": "<image>If angle A, angle B, angle C, angle D, angle E, and angle F are all depicted in the diagram, what is their sum?\nChoices:\nA: 90°\nB: 130°\nC: 180°\nD: 360°"
},
{
"from": "assistant",
"value": "<think> Okay, let's see. The problem is about two triangles: a larg... | [
"mulberry_images/geoqa_plus/10067.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-193902 | [
{
"from": "user",
"value": "<image>In the figure provided, given that the quadrilateral ABCD is inscribed in circle O such that AB is the diameter of circle O and EC is a tangent to circle O at point C, and angle ECB is 35.0 degrees, what is the measure of angle D?\nChoices:\nA: 145°\nB: 125°\nC: 90°\nD: 80... | [
"mulberry_images/geoqa_plus/4223.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-193903 | [
{
"from": "user",
"value": "<image>Consider the figure shown, where DB bisects angle ABC and DE is parallel to AB. If angle CED is 80 degrees, what is the measure of angle EDB?\nChoices:\nA: 30°\nB: 40°\nC: 60°\nD: 90°"
},
{
"from": "assistant",
"value": "<think> Okay, let me try to visualize th... | [
"mulberry_images/geoqa_plus/989.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-193904 | [
{
"from": "user",
"value": "<image>In the figure shown, if AC and DF are intersected by three parallel lines and DE:EF is in the ratio of 1.0:2.0, what is the value of AC when AB measures 2.0 units?\nChoices:\nA: 6\nB: 4\nC: 3\nD: \\frac{5}{2}"
},
{
"from": "assistant",
"value": "<think> Okay, l... | [
"mulberry_images/geoqa_plus/4880.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-193905 | [
{
"from": "user",
"value": "<image>Given that CA is perpendicular to AB in the parallelogram ABCD shown in the figure, and AB measures 5.0 while BC measures 13.0, what is the value of S~ABCD~?\nChoices:\nA: 10\nB: 26\nC: 60\nD: 65"
},
{
"from": "assistant",
"value": "<think> Okay, let's see. So ... | [
"mulberry_images/geoqa_plus/9545.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-193906 | [
{
"from": "user",
"value": "<image>In the given figure, AB represents the diameter of circle O and point C lies on circle O. If AB measures 6.0 units and angle B measures 30.0 degrees, what is the length of BC? Represent the length of BC as 'x'.\nChoices:\nA: 12\nB: 3√{3}\nC: 2√{3}\nD: 12√{3}"
},
{
... | [
"mulberry_images/geoqa_plus/8558.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-193907 | [
{
"from": "user",
"value": "<image>In triangle ABC, where AB = AC, a point P is located inside the triangle. If angle PBC is equal to angle PCA and measures 115°, what is the measure of angle A in degrees?\nChoices:\nA: 50°\nB: 55°\nC: 60°\nD: 65°"
},
{
"from": "assistant",
"value": "<think> Oka... | [
"mulberry_images/geoqa_plus/10456.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-193908 | [
{
"from": "user",
"value": "<image>If the diamond ABCD is illustrated in the figure, with AB measuring 5.0 and angle BCD measuring 120.0 degrees, what would be the perimeter of triangle ABC?\nChoices:\nA: 20\nB: 15\nC: 10\nD: 5"
},
{
"from": "assistant",
"value": "<think> Okay, let's see. The pr... | [
"mulberry_images/geoqa_plus/9136.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-193909 | [
{
"from": "user",
"value": "<image>Consider triangle ABC where sides AC, AB, and BC are all equal, with AC = AB = BD, and angle ABD measures 90°. If BC measures 6 units, what is the area of triangle BCD?\nChoices:\nA: 9\nB: 6\nC: 10\nD: 12"
},
{
"from": "assistant",
"value": "<think> Okay, let m... | [
"mulberry_images/geoqa_plus/11430.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-193910 | [
{
"from": "user",
"value": "<image>In the figure provided, parallelogram ABCD is shown. AB measures 6.0 units and AD measures 9.0 units. If the angle bisector of BAD intersects the extended line of DC at point E, what is the size of CE?\nChoices:\nA: 2\nB: 3\nC: 4\nD: 2.5"
},
{
"from": "assistant",
... | [
"mulberry_images/geoqa_plus/9370.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-193911 | [
{
"from": "user",
"value": "<image>In the given diagram, AB represents the diameter of semicircle O. AC and BC are chords, and OD is perpendicular to AC at point D. If the length of OD is 1.5, determine the length of BC. Represent the length of BC as 'x'.\nChoices:\nA: 4.5\nB: 3\nC: 2\nD: 1.5"
},
{
... | [
"mulberry_images/geoqa_plus/12206.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-193912 | [
{
"from": "user",
"value": "<image>Circle O, where AB is the diameter, is tangent to point A at PA. If OP intersects circle O at point C, connecting with CB, and angle OPA is 40.0 degrees, what is the measure of angle ABC?\nChoices:\nA: 20°\nB: 25°\nC: 30°\nD: 35°"
},
{
"from": "assistant",
"val... | [
"mulberry_images/geoqa_plus/4051.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-193913 | [
{
"from": "user",
"value": "<image>In the given figure, with AB, AC, and AD all equal in length and angle CBD measuring 44.0 degrees, what is the measure of angle CAD?\nChoices:\nA: 68°\nB: 88°\nC: 90°\nD: 112°"
},
{
"from": "assistant",
"value": "<think> Okay, so I need to find the measure of a... | [
"mulberry_images/geoqa_plus/3154.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-193914 | [
{
"from": "user",
"value": "<image>If it is known that line AB is parallel to line CD, and line BE divides angle ABC into two equal angles, and CD intersects at point D, and angle CDE measures 140 degrees, what is the measure of angle C?\nChoices:\nA: 150°\nB: 100°\nC: 130°\nD: 120°"
},
{
"from": "a... | [
"mulberry_images/geoqa_plus/901.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-193915 | [
{
"from": "user",
"value": "<image>Within the figure provided, it can be observed that circle O is circumscribed by tangents PA and PB, where A and B are the points of tangency. It is additionally mentioned that AC serves as the diameter of circle O. Given that angle P is measured as 40.0 degrees, what is t... | [
"mulberry_images/geoqa_plus/852.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-193916 | [
{
"from": "user",
"value": "<image>In the given figure, with quadrilateral ABCD inscribed in a circle, if the degree of arc BCD is 240.0, what is the measure of angle C?\nChoices:\nA: 120°\nB: 80°\nC: 60°\nD: 40°"
},
{
"from": "assistant",
"value": "<think> Okay, let's see. The problem is about ... | [
"mulberry_images/geoqa_plus/3623.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-193917 | [
{
"from": "user",
"value": "<image>What is the difference in perimeter between triangle ABD and triangle ACD if AD is the midline of triangle ABC, AB measures 5.0 units, and AC measures 3.0 units, as shown in the figure?\nChoices:\nA: 6\nB: 3\nC: 2\nD: 不确定"
},
{
"from": "assistant",
"value": "<t... | [
"mulberry_images/geoqa_plus/5245.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-193918 | [
{
"from": "user",
"value": "<image>In the given figure, where AB is the diameter of circle O and point C is positioned on the circle, if angle A is 15 degrees, what is the measure of angle BOC?\nChoices:\nA: 15°\nB: 30°\nC: 45°\nD: 75°"
},
{
"from": "assistant",
"value": "<think> Okay, let's tac... | [
"mulberry_images/geoqa_plus/8551.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-193919 | [
{
"from": "user",
"value": "<image>In the given diagram, we can observe parallelogram ABCD. Side AB measures 6.0 units, and side BC measures 10.0 units. Point E is positioned before point AD. Additionally, BE is equal to BC, and CE is equal to CD. What is the measurement of segment DE?\nChoices:\nA: 5\nB: 4... | [
"mulberry_images/geoqa_plus/9300.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-193920 | [
{
"from": "user",
"value": "<image>Triangle ABC is represented in the figure, enclosed within circle O. With an angle of 71.0 degrees at vertex ABC and an angle of 53.0 degrees at vertex CAB, and with point D positioned on the AC arc, what is the degree measure of angle ADB?\nChoices:\nA: 46°\nB: 53°\nC: 56... | [
"mulberry_images/geoqa_plus/8725.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-193921 | [
{
"from": "user",
"value": "<image>In the given figure, triangle ABC is inscribed in circle O. If angle A is 35 degrees and CD is the diameter of circle O, what is the degree measure of angle BCD?\nChoices:\nA: 55°\nB: 65°\nC: 70°\nD: 75°"
},
{
"from": "assistant",
"value": "<think> Okay, let's ... | [
"mulberry_images/geoqa_plus/3396.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-193922 | [
{
"from": "user",
"value": "<image>Given the figure, where point A is the point of tangency between line PA and circle O, and line PBC is a secant passing through O, if angle P is 30.0 degrees, what is the measure of arc AB?\nChoices:\nA: 30°\nB: 60°\nC: 90°\nD: 120°"
},
{
"from": "assistant",
"... | [
"mulberry_images/geoqa_plus/8940.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-193923 | [
{
"from": "user",
"value": "<image>As shown in the figure, P is a point outside circle O with a radius of 6.0, and PO = 12.0, two tangent lines PA and PB of circle O are made through point P. The tangent points are points A and B respectively. The area of the shaded part in the figure is ( )\nChoices:\nA:... | [
"mulberry_images/geoqa_plus/6527.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-193924 | [
{
"from": "user",
"value": "<image>Given that in the provided figure, chord AB is present in circle O and OC is the radius perpendicular to AB at point D, if OB is measured at 10.0 units and CD at 2.0 units, what is the length of AB?\nChoices:\nA: 8\nB: 12\nC: 16\nD: 20"
},
{
"from": "assistant",
... | [
"mulberry_images/geoqa_plus/5124.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-193925 | [
{
"from": "user",
"value": "<image>In the context of Rttriangle ABC, where angle C is 90.0 degrees, side AC measures 5.0 units, and side AB measures 13.0 units, what is the specific value of the cosine of angle B, indicated as 'cosB'?\nChoices:\nA: \\frac{5}{13}\nB: \\frac{12}{13}\nC: \\frac{5}{12}\nD: \\fr... | [
"mulberry_images/geoqa_plus/2734.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-193926 | [
{
"from": "user",
"value": "<image>In the figure, Xiaochao is depicted standing underneath a street lamp. Given that his height is 1.8 units, he notices that his shadow is precisely 3.0 units long. A thorough examination reveals that the distance between Xiaochao and the bottom of the street lamp is measure... | [
"mulberry_images/geoqa_plus/956.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-193927 | [
{
"from": "user",
"value": "<image>As shown in the figure, PA is the tangent of circle O, A is the tangent point, B is the intersection of OP and circle O, and C is a point on the major arc AB (not coincident with points A and B). If angle P = 36.0, then the size of angle ACB is ()\nChoices:\nA: 18°\nB: 27°... | [
"mulberry_images/geoqa_plus/4296.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-193928 | [
{
"from": "user",
"value": "<image>Considering the image supplied, which presents the overlapping of diamond ABCD and triangle ABE, wherein point D resides on line segment BE, and with the given lengths of AB, BD, and AE being 17.0, 16.0, and 25.0 respectively, what is the specific measurement of DE?\nChoic... | [
"mulberry_images/geoqa_plus/9154.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-193929 | [
{
"from": "user",
"value": "<image>Given the configuration in Figure 1, where the upper bottom surface of a paper cup 'u' is parallel to the lower bottom surface 'v', and 'w' represents the straw used to draw soybean milk from a beaker. If the measure of angle 1 is 104.0 degrees, ascertain the measure of an... | [
"mulberry_images/geoqa_plus/1163.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-193930 | [
{
"from": "user",
"value": "<image>In the parallelogram ABCD depicted below, with AE bisecting angle BAD and intersecting the DC edge at point E, DF perpendicular to AE at F, and angle ADF measuring 50.0 degrees, what is the measure of angle C?\nChoices:\nA: 85°\nB: 80°\nC: 75°\nD: 70°"
},
{
"from":... | [
"mulberry_images/geoqa_plus/9527.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-193931 | [
{
"from": "user",
"value": "<image>Given that in the figure, circle O encompasses parallelogram ABCD, with vertices A, B, and D intersecting the circle and vertex C located on the diameter BE. If angle E measures 36.0 degrees when segment AE is connected, what is the measure of angle ADC?\nChoices:\nA: 54°\... | [
"mulberry_images/geoqa_plus/3015.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-193932 | [
{
"from": "user",
"value": "<image>Provided in the figure is a scenario where a weight is being raised using a fixed pulley with a radius of 5.0 units. Point P on the pulley rotates by 108.0 degrees. Assuming no sliding occurs between the rope (excluding its thickness) and the pulley, how much higher does t... | [
"mulberry_images/geoqa_plus/614.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-193933 | [
{
"from": "user",
"value": "<image>With line l being parallel to line m and vertex B of equilateral triangle ABC positioned on line m, the acute angle between side BC and line m measures 18°. What is the degree measurement of angle α?\nChoices:\nA: 60°\nB: 42°\nC: 36°\nD: 30°"
},
{
"from": "assistan... | [
"mulberry_images/geoqa_plus/10453.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-193934 | [
{
"from": "user",
"value": "<image>Given the provided figure, with point A located east by north 45.0 at point B and west by north 15.0 at point C, what is the size of angle BAC?\nChoices:\nA: 30°\nB: 45°\nC: 50°\nD: 60°"
},
{
"from": "assistant",
"value": "<think> Okay, let's tackle this proble... | [
"mulberry_images/geoqa_plus/4953.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-193935 | [
{
"from": "user",
"value": "<image>In the figure, AB serves as the chord of circle O and CD is tangent to the circle at point B. What is the degree of angle OAB if angle ABC measures 140.0 degrees?\nChoices:\nA: 40°\nB: 45°\nC: 50°\nD: 55°"
},
{
"from": "assistant",
"value": "<think> Okay, let's... | [
"mulberry_images/geoqa_plus/3972.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-193936 | [
{
"from": "user",
"value": "<image>If angle A in the parallelogram ABCD measures 130.0 degrees and CE is perpendicular to AB with E as the foot of the perpendicular, what is the measure of angle BCE?\nChoices:\nA: 30°\nB: 40°\nC: 50°\nD: 45°"
},
{
"from": "assistant",
"value": "<think> Okay, let... | [
"mulberry_images/geoqa_plus/9571.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-193937 | [
{
"from": "user",
"value": "<image>As shown in the figure, parallel lines a and b are intersected by line c, and angle 1 = 120°. The degree of angle 2 is ()\nChoices:\nA: 50°\nB: 60°\nC: 70°\nD: 80°"
},
{
"from": "assistant",
"value": "<think> Okay, let's see. The problem is about parallel lines... | [
"mulberry_images/geoqa_plus/10855.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-193938 | [
{
"from": "user",
"value": "<image>In the triangle ABC with point D on segment AB, and angle ACD equal to angle ABC, if AC has a length of 2.0 and AD has a length of 1.0, what is the length of segment DB?\nChoices:\nA: 1\nB: 2\nC: 3\nD: 4"
},
{
"from": "assistant",
"value": "<think> Okay, let's ... | [
"mulberry_images/geoqa_plus/7664.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-193939 | [
{
"from": "user",
"value": "<image>If AB is the diameter of circle O in the provided figure, and point D lies on the extended line of AB, with DC tangent to circle O at point C, what is the degree measure of angle D if angle A is 20.0?\nChoices:\nA: 20°\nB: 30°\nC: 40°\nD: 50°"
},
{
"from": "assista... | [
"mulberry_images/geoqa_plus/9498.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-193940 | [
{
"from": "user",
"value": "<image>In the given figure, circle O contains points A, B, C, and D, with C being the midpoint of arc AB. If angle CDB measures 25.0 degrees, what is the measure of angle AOB?\nChoices:\nA: 50°\nB: 100°\nC: 125°\nD: 150°"
},
{
"from": "assistant",
"value": "<think> Ok... | [
"mulberry_images/geoqa_plus/3471.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-193941 | [
{
"from": "user",
"value": "<image>If in the given diagram of ABCD, where AE is perpendicular to BC at point E and AF is perpendicular to CD at point F, AE measures 3cm and AF measures 4cm, what is the length of BC when the perimeter of ABCD measures 56cm?\nChoices:\nA: 14cm\nB: 16cm\nC: 28cm\nD: 32cm"
},... | [
"mulberry_images/geoqa_plus/12880.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-193942 | [
{
"from": "user",
"value": "<image>In triangle ABC as shown, with angle C set at 90 degrees and point D located on CB, and DE being perpendicular to AB with a length of 2.0, alongside CA measuring 4.0, what fraction does DBAB represent?\nChoices:\nA: \\frac{1}{4}\nB: \\frac{1}{3}\nC: \\frac{1}{2}\nD: \\frac... | [
"mulberry_images/geoqa_plus/7932.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-193943 | [
{
"from": "user",
"value": "<image>Within the provided diagram, circle O is depicted with AB being its diameter. Additionally, points C and D lie on the circle but on the same side of AB. If angle ACD is established at 130.0 degrees, what is the degree measure of angle BAD?\nChoices:\nA: 50°\nB: 40°\nC: 35°... | [
"mulberry_images/geoqa_plus/3017.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-193944 | [
{
"from": "user",
"value": "<image>Given the diagram, triangle ABC is circumscribed by circle O. Connect OA and OB. If angle ABO = 35°, then the degree of angle C is ().\nChoices:\nA: 70°\nB: 65°\nC: 55°\nD: 45°"
},
{
"from": "assistant",
"value": "<think> Okay, let's see. The problem is about a... | [
"mulberry_images/geoqa_plus/10320.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-193945 | [
{
"from": "user",
"value": "<image>Provided triangle ABC, where angle A equals 90.0 degrees and AB equals 8.0 while AC equals 6.0, what is the value of cosC?\nChoices:\nA: \\frac{3}{5}\nB: \\frac{4}{5}\nC: \\frac{3}{4}\nD: \\frac{4}{3}"
},
{
"from": "assistant",
"value": "<think> Okay, so I need... | [
"mulberry_images/geoqa_plus/2571.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-193946 | [
{
"from": "user",
"value": "<image>In the figure, triangle ABC is depicted as an inscribed triangle in circle O. Point B lies on the tangent line PB of circle O, which intersects the extended line of OA at point P. Furthermore, line segment OB is connected. Given that angle P measures 34.0 degrees, what is ... | [
"mulberry_images/geoqa_plus/3850.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-193947 | [
{
"from": "user",
"value": "<image>When point C is positioned on the extended line of the diameter AB of semicircle O, with CD tangent to semicircle O at D, and DE parallel to AB intersecting the semicircle O at E, and the quadrilateral OCDE is a parallelogram with CD measuring 4.0, what is the length of ED... | [
"mulberry_images/geoqa_plus/4266.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-193948 | [
{
"from": "user",
"value": "<image>If in triangle ABC, DE is parallel to BC, AE measures 2.0, CE measures 3.0, and DE measures 4.0, what is the length of BC as shown in the figure?\nChoices:\nA: 6\nB: 10\nC: 5\nD: 8"
},
{
"from": "assistant",
"value": "<think> Okay, let's see. So there's triangl... | [
"mulberry_images/geoqa_plus/4641.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-193949 | [
{
"from": "user",
"value": "<image>When point C moves along the circle, other than points A and B, and the angle P measures 70 degrees, what is the measure of angle ACB in the scenario where points PA and PB are tangent to circle O at points A and B?\nChoices:\nA: 55度\nB: 125度\nC: 110度\nD: 55度或125度"
},
... | [
"mulberry_images/geoqa_plus/4336.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-193950 | [
{
"from": "user",
"value": "<image>Consider the figure provided, illustrating circle O with AB as its diameter. Point C is situated on the circle, and the angle bisector of BAC intersects circle O at point D. If angle ABC is measured at 40.0 degrees, what is the value of angle DBC?\nChoices:\nA: 50°\nB: 40°... | [
"mulberry_images/geoqa_plus/8807.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-193951 | [
{
"from": "user",
"value": "<image>If angle A of the parallelogram ABCD is 150 degrees, what is the size of angle C?\nChoices:\nA: 30°\nB: 75°\nC: 100°\nD: 150°"
},
{
"from": "assistant",
"value": "<think> Okay, so I need to find the measure of angle C in a parallelogram ABCD where angle A is 15... | [
"mulberry_images/geoqa_plus/10040.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-193952 | [
{
"from": "user",
"value": "<image>Given that the aircraft is at a flying height AC of 1200.0 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?\nChoices:\nA: 1200m\nB: 1200√{2}m\nC: 1200√{3}m\n... | [
"mulberry_images/geoqa_plus/6829.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-193953 | [
{
"from": "user",
"value": "<image>The given figure shows circle O with tangents PA and PB at points A and B respectively. Point C lies on circle O, and lines AC and BC are connected. If angle P equals 80.0 degrees, what is the value of angle ACB?\nChoices:\nA: 30°\nB: 40°\nC: 50°\nD: 60°"
},
{
"fro... | [
"mulberry_images/geoqa_plus/9508.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-193954 | [
{
"from": "user",
"value": "<image>If in the quadrilateral ABCD, AB is parallel to CD, AB measures 5.0, DC measures 11.0, and the sum of AD and BC is 12.0, what would be the perimeter of triangle EFG, where E, F, and G are the midpoints of BD, AC, and DC, respectively?\nChoices:\nA: 8\nB: 9\nC: 10\nD: 12"
... | [
"mulberry_images/geoqa_plus/5971.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-193955 | [
{
"from": "user",
"value": "<image>In triangle ABC, points D and E are located on sides AB and AC respectively such that AD:AC = AE:AB = 1:2. What is the length of DE if BC measures 6.0?\nChoices:\nA: 1\nB: 2\nC: 3\nD: 4"
},
{
"from": "assistant",
"value": "<think> Okay, let's see. So there's th... | [
"mulberry_images/geoqa_plus/7920.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-193956 | [
{
"from": "user",
"value": "<image>If BC is the diameter of circle O and AD is tangent to circle O at A, and angle C is given as 40.0 degrees, what is the measure of angle DAC in the figure?\nChoices:\nA: 50°\nB: 40°\nC: 25°\nD: 20°"
},
{
"from": "assistant",
"value": "<think> Okay, let me try t... | [
"mulberry_images/geoqa_plus/9916.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-193957 | [
{
"from": "user",
"value": "<image>Considering the given diagram, the straight line l serves as the tangent to circle O with tangent point A, and point B is positioned on line l. If OB intersects circle O at point C and AB is 12.0 while OA is 5.0, what is the size of BC?\nChoices:\nA: 5\nB: 6\nC: 7\nD: 8"
... | [
"mulberry_images/geoqa_plus/4081.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-193958 | [
{
"from": "user",
"value": "<image>In the given configuration, point A is the tangential point of the circle O with line PA, and point B is the tangential point of circle O with line PB. If point C is located on circle O to the right of line AB, and the measure of angle P is 36.0, then what is the measure o... | [
"mulberry_images/geoqa_plus/5506.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-193959 | [
{
"from": "user",
"value": "<image>In triangle ABC as depicted in the figure, line DE is parallel to line BC. If the ratio of AD to BD is 1:2 and the length of DE is 4.0, what is the length of BC?\nChoices:\nA: 8cm\nB: 12cm\nC: 11cm\nD: 10cm"
},
{
"from": "assistant",
"value": "<think> Okay, let... | [
"mulberry_images/geoqa_plus/4660.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-193960 | [
{
"from": "user",
"value": "<image>Given the figure provided, where line AB is parallel to line CD and triangle EFG is a right-angled triangle with angle E measuring 60 degrees, point F is the vertex of the right angle and lies on line AB. The intersection of hypotenuse EG and line AB is denoted as point H,... | [
"mulberry_images/geoqa_plus/233.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-193961 | [
{
"from": "user",
"value": "<image>Consider the figure depicting parallelogram ABCD, where the diagonals intersect at point O. Additionally, AB is not equal to AD, and line segment OE is perpendicular to BD, intersecting BD at point E. Given that the perimeter of triangle CDE is 10.0, what is the perimeter ... | [
"mulberry_images/geoqa_plus/9391.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-193962 | [
{
"from": "user",
"value": "<image>Observed in the figure is parallelogram ABCD, where AB is not equal to AD. The point of intersection between the diagonals AC and BD is labeled as O, while the line segment OE, which is perpendicular to BD, intersects AD at point E. With the perimeter of triangle ABE being... | [
"mulberry_images/geoqa_plus/9532.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-193963 | [
{
"from": "user",
"value": "<image>In parallelogram ABCD, with angle BAC denoted as alpha (alpha = 68.0) and angle ACB denoted as beta (beta = 36.0), what is the measure of angle D expressed in terms of alpha and beta?\nChoices:\nA: 86°\nB: 76°\nC: 68°\nD: 60°"
},
{
"from": "assistant",
"value":... | [
"mulberry_images/geoqa_plus/9432.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-193964 | [
{
"from": "user",
"value": "<image>As shown in the diagram, PA and PB are tangent to the circle O at points A and B respectively. Point C is a point on the circle O. Connect AC and BC. If angle P = 78°, then the degree of angle ACB is ()\nChoices:\nA: 102°\nB: 51°\nC: 41°\nD: 39°"
},
{
"from": "assi... | [
"mulberry_images/geoqa_plus/10411.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-193965 | [
{
"from": "user",
"value": "<image>In the figure, triangle ABC is circumscribed within circle O, which has diameter CD. If angle B is 50 degrees, what is the degree measure of angle ACD?\nChoices:\nA: 30°\nB: 40°\nC: 50°\nD: 60°"
},
{
"from": "assistant",
"value": "<think> Okay, let's see. The p... | [
"mulberry_images/geoqa_plus/8802.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-193966 | [
{
"from": "user",
"value": "<image>In the given triangle ABC, where D is the midpoint of BC and E is the midpoint of AC, the bisector of angle ABC intersects DE at point F. If AB measures 8 and BC measures 6, what is the length of segment EF?\nChoices:\nA: 1\nB: 2\nC: 3\nD: 4"
},
{
"from": "assistan... | [
"mulberry_images/geoqa_plus/13001.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-193967 | [
{
"from": "user",
"value": "<image>Given a quadrilateral ABCD where AC is perpendicular to BC, AD is parallel to BC, BC has a length of 3.0, AC measures 4.0, and AD measures 6.0, what is the magnitude of CM if M is positioned as the midpoint of BD?\nChoices:\nA: \\frac{3}{2}\nB: 2\nC: \\frac{5}{2}\nD: 3"
... | [
"mulberry_images/geoqa_plus/5955.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-193968 | [
{
"from": "user",
"value": "<image>Given that circle O has a radius of 4.0 and point P is on the extended line of chord AB, if OP measures 6.0 and angle APO measures 30.0 degrees, what is the length of chord AB as shown in the figure?\nChoices:\nA: √{7}\nB: 2√{7}\nC: 5\nD: 10"
},
{
"from": "assistan... | [
"mulberry_images/geoqa_plus/5102.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-193969 | [
{
"from": "user",
"value": "<image>As shown in the figure, line a is parallel to line b. The vertex of the right angle C in triangle ABC is located at an angle of 30.0 degrees along line a. If angle 1 is measured at 65.0 degrees, what is the measure of angle 2?\nChoices:\nA: 25°\nB: 30°\nC: 35°\nD: 40°"
}... | [
"mulberry_images/geoqa_plus/360.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-193970 | [
{
"from": "user",
"value": "<image>Considering the figure of quadrilateral ABCD where angle A is measured at 110 degrees and angle B is measured at 85 degrees, after folding triangle BMN along MN to get triangle FMN with MF parallel to AD and FN parallel to DC, what is the degree measurement of angle C?\nCh... | [
"mulberry_images/geoqa_plus/4923.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-193971 | [
{
"from": "user",
"value": "<image>In the figure where circle O circumscribes triangle ABC and angle B measures 62.0 degrees, what is the degree measure of angle CAO?\nChoices:\nA: 28°\nB: 30°\nC: 31°\nD: 62°"
},
{
"from": "assistant",
"value": "<think> Okay, let's see. The problem is about tria... | [
"mulberry_images/geoqa_plus/8500.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-193972 | [
{
"from": "user",
"value": "<image>Given triangle ABC and its perpendicular bisectors intersecting side BC at points D and E, with BC measuring 16 units, determine the perimeter of triangle ADE in terms of its sides and the given measurements.\nChoices:\nA: 8\nB: 16\nC: 32\nD: 0"
},
{
"from": "assis... | [
"mulberry_images/geoqa_plus/12302.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-193973 | [
{
"from": "user",
"value": "<image>If triangle ABC is shown in the figure and point D is the midpoint of side AB, such that line segment DE is constructed perpendicular to side AB and intersects side AC at point E, and point B is connected to point E, resulting in a triangle BEC with a perimeter of 15.0, an... | [
"mulberry_images/geoqa_plus/926.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-193974 | [
{
"from": "user",
"value": "<image>In the figure, triangle ABC is internally connected to circle O, with AB as the diameter and CD as the chord. If angle ADC is 55.0 degrees, what is the degree measure of angle CAB?\nChoices:\nA: 25°\nB: 35°\nC: 36°\nD: 40°"
},
{
"from": "assistant",
"value": "<... | [
"mulberry_images/geoqa_plus/5545.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-193975 | [
{
"from": "user",
"value": "<image>The figure shows triangle ABC inscribed in circle O, where AB is the diameter. If angle A equals 30 degrees, what is the degree measurement of angle ABC?\nChoices:\nA: 30°\nB: 45°\nC: 60°\nD: 75°"
},
{
"from": "assistant",
"value": "<think> Okay, let me try to ... | [
"mulberry_images/geoqa_plus/3711.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-193976 | [
{
"from": "user",
"value": "<image>In triangle ABC, DE is parallel to BC. If AD and DB have lengths of 1.0 and 2.0 respectively, what is the ratio of DE to BC?\nChoices:\nA: \\frac{2}{3}\nB: \\frac{1}{4}\nC: \\frac{1}{3}\nD: \\frac{1}{2}"
},
{
"from": "assistant",
"value": "<think> Okay, let's t... | [
"mulberry_images/geoqa_plus/7449.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-193977 | [
{
"from": "user",
"value": "<image>In triangle ABC, point D is the midpoint of segment AB and segment BE is perpendicular to segment AC with point E as the foot of the perpendicular. If segment DE measures 4 units and segment AE measures 6 units, what is the length of segment BE?\nChoices:\nA: 10\nB: 2√{5}\... | [
"mulberry_images/geoqa_plus/12855.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-193978 | [
{
"from": "user",
"value": "<image>In the provided diagram, quadrilateral ABCD has a perimeter of 36 units. Point O represents the intersection of diagonals AC and BD, while point E denotes the midpoint of CD. If the length of BD is 12 units, what is the perimeter of triangle DOE?\nChoices:\nA: 15\nB: 18\nC... | [
"mulberry_images/geoqa_plus/12110.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-193979 | [
{
"from": "user",
"value": "<image>If in the given figure, circle O has a radius of 3.0 units and points A, B, C, and D are located on it, with OA being perpendicular to BC and angle CDA measuring 30.0 degrees, what can be determined about the length of chord BC?\nChoices:\nA: \\frac{3√{3}}{2}\nB: 3√{3}\nC:... | [
"mulberry_images/geoqa_plus/1754.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-193980 | [
{
"from": "user",
"value": "<image>In the figure provided, parallelogram ABCD has a perimeter of 36.0 units. The point O represents the intersection of diagonals AC and BD. Considering that E is the midpoint of CD and BD measures 14.0 units, what is the perimeter of triangle DOE?\nChoices:\nA: 50\nB: 32\nC:... | [
"mulberry_images/geoqa_plus/9346.png"
] | vision_r1_mulberry_sft_full |
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