id stringlengths 29 36 | conversations listlengths 1 48 | images listlengths 1 1 | source_dataset stringclasses 2
values |
|---|---|---|---|
vision_r1_mulberry_sft_full-193681 | [
{
"from": "user",
"value": "<image>The figure illustrates lines AB and CD as parallel, with point E lying on line AB and line EF being perpendicular to line AB. Line EF intersects line CD at point F. If the measurement of angle 2 is 20.0 degrees, what is the degree measure of angle 1?\nChoices:\nA: 30°\nB: ... | [
"mulberry_images/geoqa_plus/1401.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-193682 | [
{
"from": "user",
"value": "<image>Suppose triangle ABC is shown in the figure, with point D lying on side BC and point O lying on side AD. If the area of triangle AOB is 3, the area of triangle BOD is 2, and the area of triangle ACO is 1, what is the area of triangle COD?\nChoices:\nA: \\frac{1}{3}\nB: 0.5... | [
"mulberry_images/geoqa_plus/11802.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-193683 | [
{
"from": "user",
"value": "<image>As shown in the figure, circle O has tangents PA and PB at points A and B respectively. Additionally, line FG intersects PA at F and PB at G and is tangent to circle O at point E. If the length of PA is 8 centimeters, what is the perimeter of triangle PFG?\nChoices:\nA: 8c... | [
"mulberry_images/geoqa_plus/12639.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-193684 | [
{
"from": "user",
"value": "<image>With reference to the given figure of rectangle ABCD, where AB is 24 units and BC is 25 units, when an arc is drawn with BC as the radius and centered at point B, intersecting side AD at point E, what is the length of EC?\nChoices:\nA: 26\nB: 28\nC: 30\nD: 32"
},
{
... | [
"mulberry_images/geoqa_plus/12075.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-193685 | [
{
"from": "user",
"value": "<image>In the provided figure, rectangle ABCD has diagonals that intersect at point O. If angle AOB measures 60° and AB measures 2, what is the length of side BC?\nChoices:\nA: 2\nB: 4\nC: 2√{3}\nD: 4√{3}"
},
{
"from": "assistant",
"value": "<think> Okay, let's try to... | [
"mulberry_images/geoqa_plus/12870.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-193686 | [
{
"from": "user",
"value": "<image>Given a rectangle ABCD and point E on side AD, connecting CE and establishing F as the midpoint of CE, what is the area of rectangle ABCD if the area of triangle BFC is 6 as indicated in the figure?\nChoices:\nA: 18\nB: 24\nC: 30\nD: 36"
},
{
"from": "assistant",
... | [
"mulberry_images/geoqa_plus/11580.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-193687 | [
{
"from": "user",
"value": "<image>If in the parallelogram ABCD, angle B is 60 degrees and the angle bisector of angle BAD intersects BC at point E, with angle AED measuring 80 degrees, what is the degree measure of angle EAC? \nChoices:\nA: 10°\nB: 15°\nC: 20°\nD: 25°"
},
{
"from": "assistant",
... | [
"mulberry_images/geoqa_plus/10022.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-193688 | [
{
"from": "user",
"value": "<image>If in the given diagram, CF is the bisector of the exterior angle angle ACM of triangle ABC and also parallel to AB, and the measure of angle ACF is 50°, then what is the measure of angle B?\nChoices:\nA: 80°\nB: 40°\nC: 60°\nD: 50°"
},
{
"from": "assistant",
"... | [
"mulberry_images/geoqa_plus/11338.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-193689 | [
{
"from": "user",
"value": "<image>If AD is parallel to BC and measures 3 units, AB measures 5 units, BC measures 9 units, and the perpendicular bisector of CD intersects BC at point E, what is the combined length of the sides of quadrilateral ABED?\nChoices:\nA: 17\nB: 18\nC: 19\nD: 20"
},
{
"from"... | [
"mulberry_images/geoqa_plus/12874.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-193690 | [
{
"from": "user",
"value": "<image>In triangle ABC, as depicted in the diagram, point D is located on side BC, and the midpoints of AD and BE are represented by E and F respectively. If the area of triangle CEF is found to be 5, what numerical value can be assigned to the area of triangle ABC?\nChoices:\nA:... | [
"mulberry_images/geoqa_plus/11979.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-193691 | [
{
"from": "user",
"value": "<image>In the diagram, triangle ABC is shown with angle ACB measuring 90° and angle B measuring 40°. Using points A and B as centers, arcs are drawn with a radius length equal to or greater than half the length of AB. The arcs intersect at points M and N. A line segment MN inters... | [
"mulberry_images/geoqa_plus/10666.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-193692 | [
{
"from": "user",
"value": "<image>In the diagram, there are two parallel lines represented as l1 and l2. A right-angle triangle board is observed to have a 30° angle. If angle 1 measures 25°, what is the measure of angle 2?\nChoices:\nA: 45°\nB: 50°\nC: 55°\nD: 60°"
},
{
"from": "assistant",
"v... | [
"mulberry_images/geoqa_plus/10738.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-193693 | [
{
"from": "user",
"value": "<image>If AB is the diameter of circle O and points C, D lie on the circle, with angle D measuring 56°, what is the size of angle ABC?\nChoices:\nA: 37°\nB: 34°\nC: 35°\nD: 36°"
},
{
"from": "assistant",
"value": "<think> Okay, let's try to figure this out. So the pro... | [
"mulberry_images/geoqa_plus/10368.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-193694 | [
{
"from": "user",
"value": "<image>In the provided diagram, triangle ABC is depicted with point D situated on side BC, where BD measures 2 units and DC measures 1 unit. Given that the area of triangle ACD is 12 square units, what is the area of triangle ABC?\nChoices:\nA: 30\nB: 36\nC: 72\nD: 24"
},
{
... | [
"mulberry_images/geoqa_plus/11976.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-193695 | [
{
"from": "user",
"value": "<image>Considering the figure where line a and line b are parallel, point B lies on line a, and AB is perpendicular to BC, what would be the measure of angle 2 if angle 1 is 35°?\nChoices:\nA: 35°\nB: 50°\nC: 55°\nD: 65°"
},
{
"from": "assistant",
"value": "<think> Ok... | [
"mulberry_images/geoqa_plus/10891.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-193696 | [
{
"from": "user",
"value": "<image>In the provided diagram, circle O is depicted with AB as its diameter, and arcs BC, CD, and DE are all equal. With angle BOC measuring 40 degrees, what is the value of angle AOE?\nChoices:\nA: 40°\nB: 60°\nC: 80°\nD: 120°"
},
{
"from": "assistant",
"value": "<t... | [
"mulberry_images/geoqa_plus/1675.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-193697 | [
{
"from": "user",
"value": "<image>Given a diagram with rectangle ABCD having diagonals AC and BD intersecting at point O, where CE is parallel to BD and DE is parallel to AC, and AC measures 6cm. What is the perimeter of quadrilateral CODE?\nChoices:\nA: 6\nB: 8\nC: 10\nD: 12"
},
{
"from": "assista... | [
"mulberry_images/geoqa_plus/12856.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-193698 | [
{
"from": "user",
"value": "<image>In the diagram featuring square ABCD, point E is positioned on the side CD. If BE measures 3 units and CE measures 1 unit, what is the length of the diagonal of square ABCD?\nChoices:\nA: 8\nB: 4√{2}\nC: 6\nD: 4"
},
{
"from": "assistant",
"value": "<think> Okay... | [
"mulberry_images/geoqa_plus/12863.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-193699 | [
{
"from": "user",
"value": "<image>Imagine a diagram showing rectangle ABCD, where the diagonals AC and BD intersect at point O. If angle AOB is determined to be 60 degrees and the length of side AB is 2 units, what would be the length of side BC?\nChoices:\nA: √{3}\nB: 2\nC: 2√{3}\nD: 4"
},
{
"from... | [
"mulberry_images/geoqa_plus/12681.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-193700 | [
{
"from": "user",
"value": "<image>In the diagram provided, triangle ABC is depicted with point D located on side AC. If it is known that angle DBC is equivalent to angle A, and the measurements of BC and AC are given as √6 and 3 units respectively, what is the value of AD?\nChoices:\nA: 2\nB: 1\nC: 1.5\nD:... | [
"mulberry_images/geoqa_plus/12572.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-193701 | [
{
"from": "user",
"value": "<image>Given the diagram where quadrilateral ABCD is depicted and has a perimeter of 14 units, with side BE measuring 2 units and side AE bisecting angle BAD and intersecting side BC at point E, what is the length of side CE?\nChoices:\nA: 1\nB: 2\nC: 3\nD: 4"
},
{
"from"... | [
"mulberry_images/geoqa_plus/12426.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-193702 | [
{
"from": "user",
"value": "<image>In the figure given, the seesaw AB is attached to the pillar OD, which intersects its midpoint O and is perpendicular to the ground BC. The point of contact with the ground is denoted as D, and OD measures 0.5 units. Assuming one end B of the seesaw touches the ground, wha... | [
"mulberry_images/geoqa_plus/1475.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-193703 | [
{
"from": "user",
"value": "<image>As shown in the figure, circle O is the circumcircle of triangle ABC. With angle OCB calculated as 40 degrees, what is the measure of angle A?\nChoices:\nA: 60°\nB: 80°\nC: 40°\nD: 50°"
},
{
"from": "assistant",
"value": "<think> Okay, let's try to figure out t... | [
"mulberry_images/geoqa_plus/1653.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-193704 | [
{
"from": "user",
"value": "<image>The provided figure shows lines AB and DG running parallel to each other. The sum of angle ADG and angle AEF is given as 180°, while line DG acts as a bisector of angle ADC. In light of this information, if angle B measures 42°, what is the degree measure of angle AEF?\nCh... | [
"mulberry_images/geoqa_plus/10803.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-193705 | [
{
"from": "user",
"value": "<image>In the figure provided, circle O encompasses quadrilateral ABCD. Furthermore, point E is located on the extended line of CD. If the measure of angle ADE is 120 degrees, what is the degree measure of angle B?\nChoices:\nA: 130°\nB: 120°\nC: 80°\nD: 60°"
},
{
"from":... | [
"mulberry_images/geoqa_plus/141.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-193706 | [
{
"from": "user",
"value": "<image>What is the measure of angle ACD if AB is the diameter of circle O and points C and D are situated on the circle, and angle DOB measures 140 degrees?\nChoices:\nA: 10°\nB: 20°\nC: 30°\nD: 40°"
},
{
"from": "assistant",
"value": "<think> Okay, let's see. So ther... | [
"mulberry_images/geoqa_plus/10217.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-193707 | [
{
"from": "user",
"value": "<image>If we have a figure depicting a quadrilateral ABCD with diagonals AC and BD intersecting at point O, and line segment OE parallel to AB intersecting AD at point E, and if OA is equal to 1 unit, what is the perimeter of ABCD if the perimeter of triangle AOE is 5 units?\nCho... | [
"mulberry_images/geoqa_plus/12675.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-193708 | [
{
"from": "user",
"value": "<image>In the diagram of triangle ABC, where AB, AC, and BC measure 7, 6, and 5 respectively, and D and E are the midpoints of sides AB and AC, what is the length of DE?\nChoices:\nA: 2.5\nB: 3\nC: 3.5\nD: 6"
},
{
"from": "assistant",
"value": "<think> Okay, so there'... | [
"mulberry_images/geoqa_plus/13043.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-193709 | [
{
"from": "user",
"value": "<image>If in the diagram of rectangle ABCD, the diagonals AC and BD intersect at point O, with angle AOD measuring 120 degrees, and the length of AB is 4, what would be the area of triangle BOC?\nChoices:\nA: 4\nB: 4√{3}\nC: 8\nD: 8√{3}"
},
{
"from": "assistant",
"val... | [
"mulberry_images/geoqa_plus/11591.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-193710 | [
{
"from": "user",
"value": "<image>Given the diagram showing triangle ABC as a paper triangle with a perimeter measuring 18cm, with circle O serving as its inscribed circle, Xiaoming plans to cut triangle AMN along any straight line MN on the right side of circle O using scissors. If the resulting cut trian... | [
"mulberry_images/geoqa_plus/12601.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-193711 | [
{
"from": "user",
"value": "<image>Let's consider the figure where diagonals AC and BD of rectangle ABCD intersect at point O. With angle ABO measuring 60° and the length of the diagonals being 6, what would be the length of segment AD?\nChoices:\nA: 3√{3}\nB: 4\nC: 2√{3}\nD: 3"
},
{
"from": "assist... | [
"mulberry_images/geoqa_plus/12926.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-193712 | [
{
"from": "user",
"value": "<image>In the figure presented, triangle ABF has an area of 2. Considering that point D is arbitrarily placed on side AB, with E and F being the respective midpoints of CD and BE, what is the area of triangle ABC?\nChoices:\nA: 4\nB: 6\nC: 8\nD: 16"
},
{
"from": "assistan... | [
"mulberry_images/geoqa_plus/11878.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-193713 | [
{
"from": "user",
"value": "<image>Consider the given diagram of triangle ABC, where angle A is 30° and angle ACB is 90°. If CD bisects angle ACB, what is the measure of angle ADC?\nChoices:\nA: 90°\nB: 100°\nC: 105°\nD: 110°"
},
{
"from": "assistant",
"value": "<think> Okay, let's tackle this g... | [
"mulberry_images/geoqa_plus/10720.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-193714 | [
{
"from": "user",
"value": "<image>Consider a diagram illustrating rectangle ABCD, where the diagonals AC and BD intersect at point O. If angle AOB is measured at 60 degrees and the length of side AB is 2 units, what is the value of side BC?\nChoices:\nA: √{3}\nB: 2\nC: 2√{3}\nD: 4"
},
{
"from": "as... | [
"mulberry_images/geoqa_plus/12681.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-193715 | [
{
"from": "user",
"value": "<image>In the provided diagram, diagonal AC of quadrilateral ABCD intersects with BD at point O. Furthermore, AB is perpendicular to AC. When AB measures 4 units and AC measures 6 units, what is the length of BD?\nChoices:\nA: 11\nB: 10\nC: 9\nD: 8"
},
{
"from": "assistan... | [
"mulberry_images/geoqa_plus/12450.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-193716 | [
{
"from": "user",
"value": "<image>Triangle ABC is shown in the figure, and it is specified that points D, E, and F are the midpoints of BC, AD, and BE respectively. Considering that the area of triangle BED is 3 square centimeters, what is the area of triangle ABC?\nChoices:\nA: 24\nB: 12\nC: 9\nD: 6"
},... | [
"mulberry_images/geoqa_plus/11939.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-193717 | [
{
"from": "user",
"value": "<image>Considering the diagram where AB is parallel to CD, CE bisects angle ACD, and angle A measures 120 degrees, find the degree measure of angle 1.\nChoices:\nA: 45°\nB: 60°\nC: 40°\nD: 30°"
},
{
"from": "assistant",
"value": "<think> Okay, let me try to work throu... | [
"mulberry_images/geoqa_plus/11153.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-193718 | [
{
"from": "user",
"value": "<image>Within the provided diagram, triangle ABC is portrayed, with point D located on side BC. Additionally, E and F stand for the midpoints of AD and BE respectively. When the line segments CE and CF are joined to form triangle CEF, which has an area of 5, what will be the area... | [
"mulberry_images/geoqa_plus/11808.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-193719 | [
{
"from": "user",
"value": "<image>Given that arcs are drawn with the three vertices of an equilateral triangle as the centers and the side length of the equilateral triangle as the radius, forming a closed curved shape known as a \"cam\", what is the perimeter of this shape if the side length of the equila... | [
"mulberry_images/geoqa_plus/12715.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-193720 | [
{
"from": "user",
"value": "<image>If triangle ABC is inscribed in circle O, with angle A measuring 35 degrees and CD as the diameter of circle O, what is the measure of angle BCD?\nChoices:\nA: 55°\nB: 65°\nC: 70°\nD: 75°"
},
{
"from": "assistant",
"value": "<think> Okay, let me try to figure t... | [
"mulberry_images/geoqa_plus/3396.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-193721 | [
{
"from": "user",
"value": "<image>If we consider a rectangle ABCD in the figure, an arc is depicted with point B as the center and AB as the radius. It intersects BC at the point P. Another arc is drawn with point D as the center and AD as the radius, intersecting BC at Q. With AB measuring 15 units and AD... | [
"mulberry_images/geoqa_plus/12813.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-193722 | [
{
"from": "user",
"value": "<image>As depicted in the figure, line PQ runs parallel to line MN. Point C is situated on line MN. Line segment CE intersects line PQ at point A, and line segment CF intersects line PQ at point B. Additionally, angle ECF is measured at 90.0 degrees. If angle FBQ is specified to ... | [
"mulberry_images/geoqa_plus/1183.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-193723 | [
{
"from": "user",
"value": "<image>Referring to the figure provided, which showcases ABCD, in which AE intersects BC at a right angle at point E, and AF intersects CD at a right angle at point F, it is known that AE measures 3cm and AF measures 4cm. If the perimeter of ABCD amounts to 56cm, what is the leng... | [
"mulberry_images/geoqa_plus/12525.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-193724 | [
{
"from": "user",
"value": "<image>Given the diagram depicting triangle ABC, point D lies on side AB. Additionally, line ED connects points E and D, while BE is parallel to AC. If angle A is equal to 56° and angle E is equal to 48°, what is the degree measure of angle ADE?\nChoices:\nA: 94°\nB: 98°\nC: 102°... | [
"mulberry_images/geoqa_plus/11227.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-193725 | [
{
"from": "user",
"value": "<image>Given that AB is parallel to CD and angle A is 124°, in triangle ACD where CE bisects angle ACD and intersects AB at point E, what is the measure of angle 1?\nChoices:\nA: 56°\nB: 38°\nC: 36°\nD: 28°"
},
{
"from": "assistant",
"value": "<think> Okay, let me try... | [
"mulberry_images/geoqa_plus/10760.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-193726 | [
{
"from": "user",
"value": "<image>Consider the figure provided, showing triangle ABC with AB perpendicular to AC. A perpendicular line AD is drawn from point A to BC, and it intersects BC at point D. If angle B measures 36 degrees, what is the degree measure of angle DAC?\nChoices:\nA: 36°\nB: 46°\nC: 54°\... | [
"mulberry_images/geoqa_plus/11345.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-193727 | [
{
"from": "user",
"value": "<image>If we consider the figure provided, illustrating rectangle ABCD with intersecting diagonals AC and BD at point O, and given that angle BOC is 120 degrees and AC measures 8 units, what information can be inferred about the length of side AB?\nChoices:\nA: 6\nB: 4\nC: 4√{3}\... | [
"mulberry_images/geoqa_plus/12667.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-193728 | [
{
"from": "user",
"value": "<image>As observed in the picture, a colossal tree was upended and collapsed during a powerful typhoon, resting at a height of 5 meters above the surface. The distance between the top of the tree trunk and its base measures 12 meters. What is the overall height of this tree?\nCho... | [
"mulberry_images/geoqa_plus/12060.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-193729 | [
{
"from": "user",
"value": "<image>In the diagram, triangle ABC is an equilateral triangle with point D located on side AC. Quadrilateral CDEF is a parallelogram, with point F positioned on the extension of line segment BC and point G as the midpoint of line segment BE. If the length of line segment AB is m... | [
"mulberry_images/geoqa_plus/12520.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-193730 | [
{
"from": "user",
"value": "<image>In the figure provided, which represents rectangle ABCD, with point G being the midpoint of AD, GE perpendicular to BG intersecting CD at point E, CE measuring the same length as CB, and the intersection of CG and BE being F, what is the measure of angle ECF?\nChoices:\nA:... | [
"mulberry_images/geoqa_plus/10692.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-193731 | [
{
"from": "user",
"value": "<image>In the provided figure, where MN is the chord of circle O and angle M is equal to 50.0 degrees, what is the measure of angle MON?\nChoices:\nA: 50°\nB: 55°\nC: 65°\nD: 80°"
},
{
"from": "assistant",
"value": "<think> Okay, so there's this circle with center O, ... | [
"mulberry_images/geoqa_plus/1674.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-193732 | [
{
"from": "user",
"value": "<image>Triangle ABC is visually portrayed in the figure, with points D, E, and F being identified as the midpoints of sides BC, AD, and CE respectively. If the area of triangle ABC amounts to 8 square centimeters, how large is the area of triangle AEF?\nChoices:\nA: 1cm2\nB: 1.5c... | [
"mulberry_images/geoqa_plus/11752.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-193733 | [
{
"from": "user",
"value": "<image>In the figure provided, right triangle ABC is depicted with angle C measuring 90 degrees. The perpendicular bisector of side AB, labeled as DE, intersects BC at point D and intersects AB at point E. When AD divides angle CAB into two angles and the ratio of angle CAD to an... | [
"mulberry_images/geoqa_plus/10001.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-193734 | [
{
"from": "user",
"value": "<image>In the given diagram, lines AB, AC, and BD are tangents to circle O, with points P, C, and D being their respective tangent points. If the length of AB is 5 units and AC is 3 units, what is the measurement of BD?\nChoices:\nA: 4\nB: 3\nC: 2\nD: 1"
},
{
"from": "ass... | [
"mulberry_images/geoqa_plus/12628.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-193735 | [
{
"from": "user",
"value": "<image>Provided is a diagram showing triangle ABC, in which D and E represent the midpoints of BC and AD respectively. Point F is situated on segment BE, and the length of EF is twice that of BF. Given that the area of triangle BCF is 2 cm^2, what is the area of triangle ABC?\nCh... | [
"mulberry_images/geoqa_plus/12000.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-193736 | [
{
"from": "user",
"value": "<image>In the diagram, AB is parallel to CD, angle 1 measures 90 degrees, and angle 2 measures 32 degrees. How many degrees does angle 3 measure?\nChoices:\nA: 68°\nB: 102°\nC: 122°\nD: 138°"
},
{
"from": "assistant",
"value": "<think> Okay, let me try to figure out t... | [
"mulberry_images/geoqa_plus/11081.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-193737 | [
{
"from": "user",
"value": "<image>Point C lies on circle O, with AB being the diameter. A tangent line passing through C intersects the extension of AB at point E. If point D is not coinciding with points A and C on AC and angle D measures 110°, what is the degree measure of angle AEC?\nChoices:\nA: 55°\nB... | [
"mulberry_images/geoqa_plus/10363.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-193738 | [
{
"from": "user",
"value": "<image>Given that the diagonals of rectangle ABCD intersect at point O in the provided diagram, it is also known that the angle bisector of angle BAD intersects BC at point E. If the measure of angle OAE is 15°, what is the measure of angle CBD?\nChoices:\nA: 30°\nB: 45°\nC: 60°\... | [
"mulberry_images/geoqa_plus/10691.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-193739 | [
{
"from": "user",
"value": "<image>As shown in the figure, in triangle ABC, AD is marked as the median of side BC. E and F represent the midpoints of AD and BE respectively. Given that the area of triangle BFD is 6, what will be the area of triangle ABC?\nChoices:\nA: 18cm2\nB: 24cm2\nC: 48cm2\nD: 72cm2"
... | [
"mulberry_images/geoqa_plus/11975.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-193740 | [
{
"from": "user",
"value": "<image>Triangle ABC is shown in the figure to be similar to triangle BDC, with the given lengths of AC as 4 units and CD as 2 units. What is the value of BC?\nChoices:\nA: 2\nB: 2√{2}\nC: 2√{3}\nD: 4"
},
{
"from": "assistant",
"value": "<think> Okay, so I have this ge... | [
"mulberry_images/geoqa_plus/12594.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-193741 | [
{
"from": "user",
"value": "<image>What is the length of BC in the given figure of a rectangle ABCD, where diagonals AC and BD intersect at point O, CD measures 3 units, and AE is perpendicular to OB and bisects it at point E?\nChoices:\nA: 4\nB: 3√{3}\nC: 6\nD: 5√{2}"
},
{
"from": "assistant",
... | [
"mulberry_images/geoqa_plus/12912.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-193742 | [
{
"from": "user",
"value": "<image>In the figure, triangle ABC is shown with AB = AC = 12, BC = 8. The angle BAC is bisected by line AD, which intersects BC at point D. E is the midpoint of AC. Calculate the perimeter of triangle CDE.\nChoices:\nA: 20\nB: 12\nC: 16\nD: 13"
},
{
"from": "assistant",
... | [
"mulberry_images/geoqa_plus/12798.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-193743 | [
{
"from": "user",
"value": "<image>If we have a rectangle named ABCD in the given figure, with side AB measuring 2 units, and a semi-circle whose diameter is equal to the length of AB that is tangent to side CD at point E, what is the total perimeter of the shaded region shown in the figure?\nChoices:\nA: 2... | [
"mulberry_images/geoqa_plus/12651.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-193744 | [
{
"from": "user",
"value": "<image>In rectangle ABCD and triangle BDE, where point A lies on side BE, and the area of the rectangle is 20 and the area of the triangle is 24, what is the area of triangle ADE?\nChoices:\nA: 10\nB: 12\nC: 14\nD: 16"
},
{
"from": "assistant",
"value": "<think> Okay,... | [
"mulberry_images/geoqa_plus/11599.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-193745 | [
{
"from": "user",
"value": "<image>In the figure depicted, triangle ABC includes an angle bisector AD and point E, which is the midpoint of AC. Line segment DE is formed by connecting point D to point E. If AB and AC measure 10 units each and BC measures 8 units, what is the perimeter of triangle CDE?\nChoi... | [
"mulberry_images/geoqa_plus/12107.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-193746 | [
{
"from": "user",
"value": "<image>In the diagram provided, AD and BE serve as medians and angle bisectors respectively for triangle ABC. If the lengths of AB and AC are equal and angle CAD is measured at 20°, what is the degree measure of angle ABE?\nChoices:\nA: 20°\nB: 35°\nC: 40°\nD: 70°"
},
{
"... | [
"mulberry_images/geoqa_plus/11310.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-193747 | [
{
"from": "user",
"value": "<image>In the provided diagram depicting rhombus OABC, with the placement of vertices A, B, and C on circle O, and the tangent to circle O passing through point B and intersecting the extension of line OA at point D, if the radius of circle O is 1 unit, what is the value of BD?\n... | [
"mulberry_images/geoqa_plus/12649.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-193748 | [
{
"from": "user",
"value": "<image>If in triangle ABC, angle C measures 90.0 degrees and the lengths of AB and BC are 3.0 and 2.0 units respectively, what is the exact value of cosB?\nChoices:\nA: \\frac{3}{5}\nB: \\frac{2}{5}\nC: \\frac{2}{3}\nD: \\frac{3}{2}"
},
{
"from": "assistant",
"value":... | [
"mulberry_images/geoqa_plus/2665.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-193749 | [
{
"from": "user",
"value": "<image>Given the figure showing triangle ABF with an area of 2, if point D is located arbitrarily on side AB, and points E and F respectively represent the midpoints of CD and BE, what is the area of triangle ABC?\nChoices:\nA: 4\nB: 6\nC: 8\nD: 16"
},
{
"from": "assistan... | [
"mulberry_images/geoqa_plus/11878.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-193750 | [
{
"from": "user",
"value": "<image>Determine the measure of angle 2 in triangle ABC, where line a is parallel to line b and vertex C, which forms a right angle with lines a and b, lies on line b. Given that the measure of angle 1 is 26 degrees.\nChoices:\nA: 26°\nB: 54°\nC: 64°\nD: 66°"
},
{
"from":... | [
"mulberry_images/geoqa_plus/10894.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-193751 | [
{
"from": "user",
"value": "<image>In the provided diagram, where angle ABC is equal to angle ACD, both measuring 90 degrees, and BC has a length of 2 units while AC and CD are also equal, what is the area of triangle BCD?\nChoices:\nA: 2\nB: 4\nC: √{6}\nD: 6"
},
{
"from": "assistant",
"value": ... | [
"mulberry_images/geoqa_plus/11816.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-193752 | [
{
"from": "user",
"value": "<image>The figure shows triangle ABC, where points D and E are located on the line segments AB and AC respectively, and the intersection of BE and CD is denoted as point F. If angle A measures 60°, angle ACD measures 40°, and angle ABE measures 30°, what is the degree measure of ... | [
"mulberry_images/geoqa_plus/11413.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-193753 | [
{
"from": "user",
"value": "<image>In the given figure, if lines AB, CD, and MN intersect at point O, and angle 1 is 22.0 degrees and angle 2 is 46.0 degrees, what is the measure of angle 3?\nChoices:\nA: 112°\nB: 102°\nC: 68°\nD: 46°"
},
{
"from": "assistant",
"value": "<think> Okay, so we have... | [
"mulberry_images/geoqa_plus/1101.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-193754 | [
{
"from": "user",
"value": "<image>With reference to the diagram depicting triangle ABC, where points D, E, and F are identified as the midpoints of BC, AD, and BE respectively, and where the area of triangle BED is stated as 3 square centimeters, what is the area of triangle ABC?\nChoices:\nA: 24\nB: 12\nC... | [
"mulberry_images/geoqa_plus/11886.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-193755 | [
{
"from": "user",
"value": "<image>In the provided figure, consider quadrilateral ABCD. The length of AB is 3 units and BC is 5 units. The bisector of angle ABC intersects side AD at point E. Find the length of DE.\nChoices:\nA: 5\nB: 4\nC: 3\nD: 2"
},
{
"from": "assistant",
"value": "<think> Ok... | [
"mulberry_images/geoqa_plus/12461.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-193756 | [
{
"from": "user",
"value": "<image>As illustrated in the diagram, the diagonals of rectangle ABCD intersect at point O. Moreover, the intersection of the angle bisector of angle BAD and BC is point E. If the measure of angle OAE is 15°, what is the measure of angle CBD?\nChoices:\nA: 30°\nB: 45°\nC: 60°\nD:... | [
"mulberry_images/geoqa_plus/10691.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-193757 | [
{
"from": "user",
"value": "<image>Given the information that triangle ABC has an area of 8 and point D is arbitrarily chosen on side AB, determine the area of triangle ABF with the knowledge that E is the midpoint of CD and F is the midpoint of BE.\nChoices:\nA: 3\nB: 2\nC: 2.5\nD: 1"
},
{
"from": ... | [
"mulberry_images/geoqa_plus/12014.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-193758 | [
{
"from": "user",
"value": "<image>If circle O is the circumcircle of a regular hexagon ABCDEF and point P is situated on arc AB, what is the measure of angle CPD?\nChoices:\nA: 30°\nB: 40°\nC: 45°\nD: 60°"
},
{
"from": "assistant",
"value": "<think> Okay, let me try to figure this out. So, ther... | [
"mulberry_images/geoqa_plus/10659.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-193759 | [
{
"from": "user",
"value": "<image>What is the value of side BC in rectangle ABCD, as shown in the figure where angle AOB is 60 degrees, AC measures 4 units, and the diagonals intersect at point O?\nChoices:\nA: 2\nB: 3\nC: 2√{3}\nD: 3√{2}"
},
{
"from": "assistant",
"value": "<think> Okay, so I ... | [
"mulberry_images/geoqa_plus/12900.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-193760 | [
{
"from": "user",
"value": "<image>By referring to the figure, in triangle ABC, points D, E, and F serve as the midpoints of BC, AD, and BE respectively. Given that the area of triangle BED is 3 square centimeters, what is the area of triangle ABC?\nChoices:\nA: 24\nB: 12\nC: 9\nD: 6"
},
{
"from": "... | [
"mulberry_images/geoqa_plus/11939.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-193761 | [
{
"from": "user",
"value": "<image>In the given diagram, with quadrilateral ABCD illustrated and BC measuring 10, AC measuring 8, and BD measuring 14, what will be the perimeter of triangle AOD?\nChoices:\nA: 16\nB: 20\nC: 21\nD: 23"
},
{
"from": "assistant",
"value": "<think> Okay, so I need to... | [
"mulberry_images/geoqa_plus/12092.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-193762 | [
{
"from": "user",
"value": "<image>In the included diagram, triangle ABC is presented with angle A measuring 60 degrees and the length of BC measuring 6 units. The perimeter of the triangle is 16 units. If circle O intersects sides BC, AC, and AB at points E, F, and D respectively, what distance does DF rep... | [
"mulberry_images/geoqa_plus/12638.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-193763 | [
{
"from": "user",
"value": "<image>Point E lies on side AD of rectangle ABCD, with CE being connected and F being the midpoint of CE. If the area of triangle BFC is 6, what is the area of rectangle ABCD as shown in the figure?\nChoices:\nA: 18\nB: 24\nC: 30\nD: 36"
},
{
"from": "assistant",
"val... | [
"mulberry_images/geoqa_plus/11580.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-193764 | [
{
"from": "user",
"value": "<image>In the diagram, it is shown that line AB is parallel to line CD, and angle BEG is bisected by line EF. Given that angle 1 is 50 degrees, what is the degree measurement of angle 2?\nChoices:\nA: 55°\nB: 60°\nC: 65°\nD: 70°"
},
{
"from": "assistant",
"value": "<t... | [
"mulberry_images/geoqa_plus/11118.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-193765 | [
{
"from": "user",
"value": "<image>As depicted in the figure, the positions of the straight lines a, b, c, and d are shown. Given that angle 1 and angle 2 are both equal to 90 degrees, and angle 3 is measured at 42 degrees, what is the measure of angle 4?\nChoices:\nA: 130°\nB: 138°\nC: 140°\nD: 142°"
},
... | [
"mulberry_images/geoqa_plus/1366.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-193766 | [
{
"from": "user",
"value": "<image>In the process of measuring the thickness of a small circular container, Xiaoming utilized the \"X-type rotary pliers\" and followed the method illustrated in the figure. During the measurement, it was discovered that OA is equal to OD, OB is equal to OC, AB equals 5 centi... | [
"mulberry_images/geoqa_plus/12539.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-193767 | [
{
"from": "user",
"value": "<image>As depicted in the figure, AB is parallel to CD, angle EFD equals 64°, and the angle bisector of angle FEB intersects CD at point G. Determine the value of angle EGF.\nChoices:\nA: 66°\nB: 56°\nC: 68°\nD: 58°"
},
{
"from": "assistant",
"value": "<think> Okay, l... | [
"mulberry_images/geoqa_plus/10733.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-193768 | [
{
"from": "user",
"value": "<image>In the figure showing angle AOB measuring 90 degrees, angle EOD measures 60 degrees as OE bisects angle AOB and OD bisects angle BOC. Find the measure of angle EOC.\nChoices:\nA: 75°\nB: 90°\nC: 30°\nD: 45°"
},
{
"from": "assistant",
"value": "<think> Okay, let... | [
"mulberry_images/geoqa_plus/10944.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-193769 | [
{
"from": "user",
"value": "<image>In the provided figure, there is a quadrilateral ABCD. The measurements of its sides are AB = 2, BC = 2, CD = 4, and DA = 2√6. Moreover, angle ABC is equal to 90 degrees. Find the area enclosed by quadrilateral ABCD.\nChoices:\nA: 4\nB: 1+2√{2}\nC: 2+4√{2}\nD: 1+√{2}"
},... | [
"mulberry_images/geoqa_plus/11376.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-193770 | [
{
"from": "user",
"value": "<image>What is the area of triangle ABC if point D is on side BC of the triangle, and F, G, and E are the midpoints of AD, BF, and CF respectively, and the area of triangle FGE is 8?\nChoices:\nA: 32\nB: 48\nC: 64\nD: 72"
},
{
"from": "assistant",
"value": "<think> Ok... | [
"mulberry_images/geoqa_plus/11517.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-193771 | [
{
"from": "user",
"value": "<image>If we have triangle ABC, where angle B is a right angle and AB and BC measure 12 units and 5 units respectively, and a point D moves along AC, resulting in DE being perpendicular to AB at E and DF perpendicular to BC at F, what is the minimum length of EF?\nChoices:\nA: 4.... | [
"mulberry_images/geoqa_plus/12544.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-193772 | [
{
"from": "user",
"value": "<image>Located on the sides AB and CD of quadrilateral ABCD, points E and F are shown in the figure. The intersection of AF and DE is at point P, and the intersection of BF and CE is at point Q. Given that the triangle APD has an area of 15 and triangle BQC has an area of 25, wha... | [
"mulberry_images/geoqa_plus/11459.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-193773 | [
{
"from": "user",
"value": "<image>In the given figure depicting rectangle ABCD, if angle AOB is measured at 60 degrees and AB is 3 units, what would be the length of BD?\nChoices:\nA: 3\nB: 5\nC: 3√{3}\nD: 6"
},
{
"from": "assistant",
"value": "<think> Okay, so I have this problem about a recta... | [
"mulberry_images/geoqa_plus/12943.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-193774 | [
{
"from": "user",
"value": "<image>In the given diagram, line a is parallel to line b, and line l intersects lines a and b at points A and B respectively. Additionally, the line perpendicular to line l that passes through point A intersects line b at point C. If angle 1 measures 32°, what is the degree meas... | [
"mulberry_images/geoqa_plus/10756.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-193775 | [
{
"from": "user",
"value": "<image>In the provided diagram, where trapezoid ABCD is depicted with AB being parallel to CD, point E serves as the midpoint of BC, and EF is perpendicular to AD at point F, if AD measures 4 units and EF measures 5 units, what is the area of trapezoid ABCD?\nChoices:\nA: 40\nB: ... | [
"mulberry_images/geoqa_plus/11728.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-193776 | [
{
"from": "user",
"value": "<image>What is the value of tan(angle ABC) in the 4x5 square grid, as depicted in the figure, where each small square has a side length of 1 and the vertices of triangle ABC are positioned on the grid points of these small squares?\nChoices:\nA: \\frac{3√5}{5}\nB: \\frac{√17}{5}\... | [
"mulberry_images/geoqa_plus/10620.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-193777 | [
{
"from": "user",
"value": "<image>If in the figure, triangle ABC has angle ACB measuring 90 degrees, D is the midpoint of side AB, CE is perpendicular to AB at E, and the lengths are CE = 5 and CD = 6, what is the area of triangle ABC?\nChoices:\nA: 60\nB: 50\nC: 40\nD: 30"
},
{
"from": "assistant"... | [
"mulberry_images/geoqa_plus/11586.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-193778 | [
{
"from": "user",
"value": "<image>In triangle ABC, with angle C equal to 90 degrees, an arc with vertex A as the center and an appropriate radius is drawn, intersecting AC and AB at points M and N respectively. Following this, arcs are drawn with centers at points M and N, having a radius greater than 0.5 ... | [
"mulberry_images/geoqa_plus/11426.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-193779 | [
{
"from": "user",
"value": "<image>In the figure provided, where triangle ABF has an area of 2 units and point D lies on side AB, point E is the midpoint of CD, and point F is the midpoint of BE, what is the area of triangle ABC?\nChoices:\nA: 4\nB: 6\nC: 8\nD: 16"
},
{
"from": "assistant",
"val... | [
"mulberry_images/geoqa_plus/11838.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-193780 | [
{
"from": "user",
"value": "<image>In the provided figure, where AB is the diameter of circle O, point D lies on circle O, angle ABD is measured at 30 degrees, and BO is 4.0 units long, what is the length of AD?\nChoices:\nA: 3\nB: 4\nC: 4√{3}\nD: 8"
},
{
"from": "assistant",
"value": "<think> O... | [
"mulberry_images/geoqa_plus/1842.png"
] | vision_r1_mulberry_sft_full |
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