id stringlengths 29 36 | conversations listlengths 1 48 | images listlengths 1 1 | source_dataset stringclasses 2
values |
|---|---|---|---|
vision_r1_mulberry_sft_full-194581 | [
{
"from": "user",
"value": "<image>If we have a rectangle ABCD with O as the midpoint of diagonal AC and M as the midpoint of side CD, and AB measures 12 units while OM measures 4.5 units, what will be the length of segment OB?\nChoices:\nA: 7\nB: 8\nC: 7.5\nD: 8"
},
{
"from": "assistant",
"valu... | [
"mulberry_images/geoqa_plus/12940.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194582 | [
{
"from": "user",
"value": "<image>Given the diagram depicting triangle ABF, with an area of 2 units, if point D is located on side AB, point E is the midpoint of side CD, and point F is the midpoint of side BE, what is the area of triangle ABC?\nChoices:\nA: 4\nB: 6\nC: 8\nD: 16"
},
{
"from": "assi... | [
"mulberry_images/geoqa_plus/11990.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194583 | [
{
"from": "user",
"value": "<image>In the provided figure, a ruler and a right-angle triangle plate with a measurement of 30.0 are positioned, and angle 1 measures 34.0 degrees. What is the degree value of angle 2?\nChoices:\nA: 114°\nB: 124°\nC: 116°\nD: 126°"
},
{
"from": "assistant",
"value":... | [
"mulberry_images/geoqa_plus/1362.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194584 | [
{
"from": "user",
"value": "<image>In the given diagram, the diamond ABCD is depicted with AC and BD as its diagonals, which intersect at point O. Through point A, a line is drawn perpendicular to BC, with the intersection point labeled as H. Connecting point O and point H forms the line segment OH. If OB m... | [
"mulberry_images/geoqa_plus/12827.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194585 | [
{
"from": "user",
"value": "<image>If in rectangle ABCD, AB measures 3 units and the diagonals AC and BD intersect at point O, where AE is a perpendicular line that bisects OB at point E, what is the value of AD?\nChoices:\nA: 4\nB: 3√{3}\nC: 5\nD: 5√{2}"
},
{
"from": "assistant",
"value": "<thi... | [
"mulberry_images/geoqa_plus/12946.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194586 | [
{
"from": "user",
"value": "<image>What is the length of side BC in triangle ABC if D and E are the midpoints of sides AB and AC, and DE measures 6 units?\nChoices:\nA: 18\nB: 12\nC: 10\nD: 8"
},
{
"from": "assistant",
"value": "<think> Okay, so there's this triangle ABC, and D and E are the mid... | [
"mulberry_images/geoqa_plus/13024.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194587 | [
{
"from": "user",
"value": "<image>Imagining the figure presented, where rhombus ABCD is illustrated, with the diagonals AC and BD intersecting at point O and M serving as the midpoint of side AB, if the length of MO is given as 4cm, what would be the perimeter of rhombus ABCD?\nChoices:\nA: 32cm\nB: 24cm\n... | [
"mulberry_images/geoqa_plus/12073.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194588 | [
{
"from": "user",
"value": "<image>Given the figure depicting quadrilateral ABCD, with BC measuring 13 units, point A extended to point E such that line AE is perpendicular to line DC at point E, and AE measuring 12 units while EC measures 10 units, what is the numerical value of AB?\nChoices:\nA: 11\nB: 15... | [
"mulberry_images/geoqa_plus/12468.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194589 | [
{
"from": "user",
"value": "<image>Given the diagram of triangle ABC, where F is the midpoint of BC and E is located on side AC, and AC measures 10 units, what is the length of AE?\nChoices:\nA: 3\nB: 4\nC: 5\nD: 4.5"
},
{
"from": "assistant",
"value": "<think> Okay, let's tackle this problem. S... | [
"mulberry_images/geoqa_plus/12672.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194590 | [
{
"from": "user",
"value": "<image>Looking at the given diagram, circle O is shown with diameter BC. Chord AD intersects BC at point E, creating a right angle. Line l is tangent to circle O at point C, and line OD extends to intersect line l at point F. If AE is measured as 2 units and angle ABC is 22.5 deg... | [
"mulberry_images/geoqa_plus/12602.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194591 | [
{
"from": "user",
"value": "<image>In the provided diagram, while measuring the distance between points A and B on the edge of the pond, Xiao Ming selected point O on one side of the pond. After observing that point D is the midpoint of OA and point E is the midpoint of OB, with DE measuring 14 meters, what... | [
"mulberry_images/geoqa_plus/13045.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194592 | [
{
"from": "user",
"value": "<image>In triangle ABC shown in the diagram, F is the midpoint of BC and E lies on side AC. If the length of AC is 10 units, what is the length of AE?\nChoices:\nA: 3\nB: 4\nC: 5\nD: 4.5"
},
{
"from": "assistant",
"value": "<think> Okay, so I need to find the length o... | [
"mulberry_images/geoqa_plus/12672.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194593 | [
{
"from": "user",
"value": "<image>Given triangle ABC with AB = BC = √{3} and angle BAC at 30°, points A and C are used as centers to draw arcs with AC as the radius, intersecting at point D. What is the area of quadrilateral ABCD when DA and DC are connected?\nChoices:\nA: 6√{3}\nB: 9\nC: 6\nD: 3√{3}"
},... | [
"mulberry_images/geoqa_plus/11545.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194594 | [
{
"from": "user",
"value": "<image>With the presence of a pond separating points A and C, Mr. Li chooses a point B outside of AC and connects BA and BC. Upon identifying the midpoints E and F, the measured distance between E and F is 25 meters. What is the distance between points A and C as a result?\nChoic... | [
"mulberry_images/geoqa_plus/13065.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194595 | [
{
"from": "user",
"value": "<image>Referencing the diagram provided, where lines PA and PB intersect circle O at points A and B, and line CD intersects circle O at point E and intersects lines PA and PB at points C and D, if the length of PA is 12, what is the circumference of triangle PCD?\nChoices:\nA: 12... | [
"mulberry_images/geoqa_plus/12626.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194596 | [
{
"from": "user",
"value": "<image>In the figure provided, quadrilateral ABCD is shown with angle DAB measuring 90° and angle DCB measuring 90°. Points E and F represent the midpoints of BD and AC respectively. When AC is 6 units in length and BD is 10 units in length, what is the length of EF?\nChoices:\nA... | [
"mulberry_images/geoqa_plus/12844.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194597 | [
{
"from": "user",
"value": "<image>Considering a V-shaped frame holding a steel pipe with a radius of 24cm, if angle ACB is 60 degrees, what is the length of arc AB?\nChoices:\nA: 8πcm\nB: 16πcm\nC: 32πcm\nD: 192πcm"
},
{
"from": "assistant",
"value": "<think> Okay, let's see. The problem is abo... | [
"mulberry_images/geoqa_plus/12706.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194598 | [
{
"from": "user",
"value": "<image>Given the diagram showing quadrilateral ABCD as a rhombus, with AC measuring 8cm and DB measuring 6cm, and with DH perpendicular to AB at point H, what is the length of DH?\nChoices:\nA: 3.6\nB: 4.8\nC: 5\nD: 10"
},
{
"from": "assistant",
"value": "<think> Okay... | [
"mulberry_images/geoqa_plus/12099.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194599 | [
{
"from": "user",
"value": "<image>In the given diagram, if O is the midpoint of diagonal AC in rectangle ABCD, M is the midpoint of AD, and BC measures 8 while OB measures 5, what is the length of OM?\nChoices:\nA: 1\nB: 2\nC: 3\nD: 4"
},
{
"from": "assistant",
"value": "<think> Okay, let's see... | [
"mulberry_images/geoqa_plus/12955.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194600 | [
{
"from": "user",
"value": "<image>In the provided diagram, with a perimeter of 20cm, diamond ABCD has one diagonal, AC, measuring 6cm. What is the length of diagonal BD?\nChoices:\nA: 4cm\nB: 6cm\nC: 8cm\nD: 10cm"
},
{
"from": "assistant",
"value": "<think> Okay, let's tackle this problem step ... | [
"mulberry_images/geoqa_plus/12674.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194601 | [
{
"from": "user",
"value": "<image>In the figure provided, let AB be the diameter of circle O, BC be a tangent to circle O at point B, AB measuring 8 units, and the tangent of angle BAC being 0.75. Find the length of BC.\nChoices:\nA: 8\nB: 7\nC: 10\nD: 6"
},
{
"from": "assistant",
"value": "<th... | [
"mulberry_images/geoqa_plus/12708.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194602 | [
{
"from": "user",
"value": "<image>Consider the rectangle ABCD depicted in the diagram, where the diagonals AC and BD intersect at point O. If the measure of angle AOB is 60 degrees and the length of BD is 6 units, what is the length of side AB?\nChoices:\nA: 1.5\nB: 3\nC: √{3}\nD: 2√{3}"
},
{
"from... | [
"mulberry_images/geoqa_plus/12938.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194603 | [
{
"from": "user",
"value": "<image>Given that diamond ABCD has a perimeter of 20cm and diagonal AC measures 6cm, what is the length of diagonal BD?\nChoices:\nA: 4cm\nB: 6cm\nC: 8cm\nD: 10cm"
},
{
"from": "assistant",
"value": "<think> Okay, so I need to find the length of diagonal BD in this di... | [
"mulberry_images/geoqa_plus/12674.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194604 | [
{
"from": "user",
"value": "<image>In the diagram showing triangle ABC with angle C measuring 90°, and AD bisecting angle BAC and intersecting side BC at point D, if AB measures 10 units and CD is 3 units, what is the area of triangle ABD?\nChoices:\nA: 15\nB: 30\nC: 10\nD: 20"
},
{
"from": "assista... | [
"mulberry_images/geoqa_plus/11541.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194605 | [
{
"from": "user",
"value": "<image>In the figure presented, where points E and F are the midpoints of sides BD and CE respectively and the area of triangle AEF is 3, what would be the area of triangle ABC?\nChoices:\nA: 9\nB: 10\nC: 11\nD: 12"
},
{
"from": "assistant",
"value": "<think> Okay, so... | [
"mulberry_images/geoqa_plus/11969.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194606 | [
{
"from": "user",
"value": "<image>Let's consider the figure where paper strips are aligned parallel to the two edges of the right angle triangle. If angle 1 is known to be 60.0 degrees, what can be deduced about the measure of angle 2?\nChoices:\nA: 60°\nB: 45°\nC: 50°\nD: 30°"
},
{
"from": "assist... | [
"mulberry_images/geoqa_plus/1336.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194607 | [
{
"from": "user",
"value": "<image>In the given figure, triangle ABC is an equilateral triangle, with point D as the intersection of line segment AD and BC, where AD is perpendicular to BC. If angle CED is measured as 50.0 degrees and point E is on AD, what is the measure of angle ABE?\nChoices:\nA: 10°\nB:... | [
"mulberry_images/geoqa_plus/1244.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194608 | [
{
"from": "user",
"value": "<image>If angle AOB measures 60 degrees and AB is 3 units in rectangle ABCD, what is the length of BD?\nChoices:\nA: 3\nB: 5\nC: 3√{3}\nD: 6"
},
{
"from": "assistant",
"value": "<think> Okay, let's tackle this problem step by step. So, we have a rectangle ABCD with di... | [
"mulberry_images/geoqa_plus/12943.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194609 | [
{
"from": "user",
"value": "<image>In the provided figure, points A, B, and C are all on circle O. If the measure of angle AOB is 72.0 degrees, what is the degree measure of angle ACB?\nChoices:\nA: 18°\nB: 36°\nC: 54°\nD: 72°"
},
{
"from": "assistant",
"value": "<think> Okay, so I need to find ... | [
"mulberry_images/geoqa_plus/1312.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194610 | [
{
"from": "user",
"value": "<image>What is the length of diagonal AC in rectangle ABCD, where the intersection of lines AC and BD is denoted by point O and angle AOB is given as 60°, with AB measuring 5 units?\nChoices:\nA: 5\nB: 7.5\nC: 10\nD: 15"
},
{
"from": "assistant",
"value": "<think> Oka... | [
"mulberry_images/geoqa_plus/12857.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194611 | [
{
"from": "user",
"value": "<image>Given a figure depicting rhombus ABCD, where diagonal AC and BD intersect at point O and H is the midpoint of side AD, if the perimeter of the rhombus is known to be 28 units, can you determine the length of OH?\nChoices:\nA: 3.5\nB: 4.5\nC: 7\nD: 14"
},
{
"from": ... | [
"mulberry_images/geoqa_plus/12126.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194612 | [
{
"from": "user",
"value": "<image>Considering the diagram of parallelogram ABCD, with a perpendicular line drawn from point A to BC at G and another perpendicular line drawn from point A to CD at H, and the given angle GAH measuring 45 degrees, AG measuring 2, and AH measuring 3, what is the area of the pa... | [
"mulberry_images/geoqa_plus/11466.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194613 | [
{
"from": "user",
"value": "<image>In the given figure, where triangle PBC has an area of 15 square centimeters, if PB bisects angle ABC and AP intersects BP at point P forming a right angle, what is the area of triangle ABC?\nChoices:\nA: 25cm2\nB: 30cm2\nC: 32.5cm2\nD: 35cm2"
},
{
"from": "assista... | [
"mulberry_images/geoqa_plus/11875.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194614 | [
{
"from": "user",
"value": "<image>Consider the figure shown, where triangle ABC is a right triangle and the median CD is drawn on the hypotenuse AB. If AB measures 8 units, what is the length of CD?\nChoices:\nA: 6\nB: 5\nC: 4\nD: 3"
},
{
"from": "assistant",
"value": "<think> Okay, so I need t... | [
"mulberry_images/geoqa_plus/12763.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194615 | [
{
"from": "user",
"value": "<image>As illustrated, the diagonals AC and BD of parallelogram ABCD intersect at point O. AB is perpendicular to AC, with AB measuring 8 units and BD measuring 20 units. What is the length of AC in the provided figure?\nChoices:\nA: 6\nB: 10\nC: 12\nD: 18"
},
{
"from": "... | [
"mulberry_images/geoqa_plus/12431.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194616 | [
{
"from": "user",
"value": "<image>With the area of triangle ABC known to be 16cm^2, what is the area of triangle PBC if point P lies on the intersection of AP, perpendicular to the bisector of angle B, and BP?\nChoices:\nA: 7\nB: 8\nC: 9\nD: 10"
},
{
"from": "assistant",
"value": "<think> Okay,... | [
"mulberry_images/geoqa_plus/11419.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194617 | [
{
"from": "user",
"value": "<image>Triangle ABC is showcased in the figure with BD functioning as its median. E and F represent the midpoints of BD and CE, respectively. If it is known that the area of triangle AEF is exactly 3, what is the area of triangle ABC?\nChoices:\nA: 9\nB: 10\nC: 11\nD: 12"
},
... | [
"mulberry_images/geoqa_plus/11907.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194618 | [
{
"from": "user",
"value": "<image>The figure illustrates a rhombus ABCD, wherein BC is measured to be 10 units. On line segment BD, we can find a point E, while F serves as the midpoint of line segment AD. Alongside this, line segment FE is perpendicular to BD with E as the foot, and the length of EF is 4 ... | [
"mulberry_images/geoqa_plus/12747.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194619 | [
{
"from": "user",
"value": "<image>Given a figure showing right triangle ABC, with angle ACB equal to 90 degrees, CD being perpendicular to AB and D being the point where the perpendicular intersects AB, what is the magnitude of length CB if AD measures 8 units and DB is 2 units?\nChoices:\nA: 2√{5}\nB: 4\n... | [
"mulberry_images/geoqa_plus/12597.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194620 | [
{
"from": "user",
"value": "<image>If in the figure, AF is the bisector of angle BAC and FD is drawn perpendicular to BC, and the measure of angle B is 20.0 degrees greater than angle C, what is the measure of angle F?\nChoices:\nA: 10°\nB: 15°\nC: 20°\nD: 不能确定"
},
{
"from": "assistant",
"value"... | [
"mulberry_images/geoqa_plus/124.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194621 | [
{
"from": "user",
"value": "<image>In the given figure, point O represents the intersection of diagonals AC and BD in parallelogram ABCD. If AB creates a right angle with AC and AB has a length of 8 units, while BD has a length of 20 units, what is the length of AC?\nChoices:\nA: 6\nB: 10\nC: 12\nD: 18"
}... | [
"mulberry_images/geoqa_plus/12431.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194622 | [
{
"from": "user",
"value": "<image>In the provided figure, point A and point B are positioned on line l1, while point C and point D are positioned on line l2. The lines l1 and l2 are parallel. Additionally, CA is perpendicular to l1, BD is perpendicular to l2, and AC measures 3cm. What is the length of BD? ... | [
"mulberry_images/geoqa_plus/12927.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194623 | [
{
"from": "user",
"value": "<image>The diagram illustrates an equilateral triangle denoted as ABC, where D and E are the midpoints of sides AB and BC, respectively. If the length of DE is 2 units, what will be the perimeter of triangle ABC?\nChoices:\nA: 9\nB: 12\nC: 16\nD: 18"
},
{
"from": "assista... | [
"mulberry_images/geoqa_plus/12081.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194624 | [
{
"from": "user",
"value": "<image>Given triangle ABC in the figure provided, where point D is located on side BC, and points E and F are the midpoints of AD and CE respectively, if the area of triangle BEF is 3, what is the area of triangle ABC?\nChoices:\nA: 9\nB: 10\nC: 11\nD: 12"
},
{
"from": "a... | [
"mulberry_images/geoqa_plus/11849.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194625 | [
{
"from": "user",
"value": "<image>In the diagram provided, triangle ABC is an equilateral triangle with point D marking the intersection of line segment AD and BC, where AD is perpendicular to BC. If angle CED measures 50.0 degrees and point E lies on AD, what is the degree measure of angle ABE?\nChoices:\... | [
"mulberry_images/geoqa_plus/1244.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194626 | [
{
"from": "user",
"value": "<image>In the provided diagram of rectangle ABCD, the intersection of diagonal AC and diagonal BD is marked as point O. If angle ADB is equal to 30 degrees and AB measures 4 units, what is the magnitude of OC?\nChoices:\nA: 5\nB: 4\nC: 3.5\nD: 3"
},
{
"from": "assistant",... | [
"mulberry_images/geoqa_plus/12865.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194627 | [
{
"from": "user",
"value": "<image>Point O is the intersection of diagonals AC and BD in rectangle ABCD, as shown in the figure. If angle ABO is 60° and the length of the diagonals is 6, what is the length of segment AD?\nChoices:\nA: 3√{3}\nB: 4\nC: 2√{3}\nD: 3"
},
{
"from": "assistant",
"value... | [
"mulberry_images/geoqa_plus/12926.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194628 | [
{
"from": "user",
"value": "<image>Within the figure provided, quadrilateral ABCD is represented. It is worth noting that AC is a line connecting points A and C. Given the information that angle ABC and angle CAD both measure 60 degrees, and that AB equals 3 units in length, what can be said about the lengt... | [
"mulberry_images/geoqa_plus/12109.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194629 | [
{
"from": "user",
"value": "<image>Given a rectangle with adjacent sides measuring 1 and 2, what is the length of its diagonal?\nChoices:\nA: √{3}\nB: √{5}\nC: 3\nD: 2√{2}"
},
{
"from": "assistant",
"value": "<think> Okay, let's see. The problem is about finding the length of the diagonal in a r... | [
"mulberry_images/geoqa_plus/12678.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194630 | [
{
"from": "user",
"value": "<image>Given a ladder with a length of 2.5 units, where one end is placed 1.5 units away from the corner of the wall, and the other end rests against the wall, what is the distance between the top of the ladder and the corner of the wall?\nChoices:\nA: 0.2米\nB: 0.4米\nC: 2米\nD: 4米... | [
"mulberry_images/geoqa_plus/1538.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194631 | [
{
"from": "user",
"value": "<image>In the given figure, which shows point P positioned on the exterior of circle O, PA serves as a tangent line to circle O at point A, with line PO intersecting circle O at point B, and angle P measuring 30 degrees, what is the length of segment AP if BP is 4 units long?\nCh... | [
"mulberry_images/geoqa_plus/12653.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194632 | [
{
"from": "user",
"value": "<image>In triangle ABC, which is illustrated in the diagram, point E is positioned on side BC so that EC is equal to three times the length of BE. Furthermore, point D serves as the midpoint of side AC. On the basis that the area of triangle ABC is known to be 36, what is the cal... | [
"mulberry_images/geoqa_plus/11796.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194633 | [
{
"from": "user",
"value": "<image>Given the figure representing a circle O with a radius of 1 and a tangent line passing through point P, which intersects the circle at points A and B. If angle APB measures 60 degrees, what is the length of PA?\nChoices:\nA: √{2}\nB: 2\nC: √{3}\nD: 3"
},
{
"from": ... | [
"mulberry_images/geoqa_plus/12605.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194634 | [
{
"from": "user",
"value": "<image>Given the figure, triangle ABC is displayed. Point D is an arbitrary point on the side BC, and the midpoints of line segments AD and CE are points E and F respectively. If the area of triangle ABC is 1, what is the area of triangle BEF?\nChoices:\nA: 0.5\nB: \\frac{1}{3}\n... | [
"mulberry_images/geoqa_plus/11759.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194635 | [
{
"from": "user",
"value": "<image>Within the provided figure, triangle PBC has an area equal to 15 square centimeters. Given that PB serves as the bisector of angle ABC and AP intersects BP at a right angle at point P, what is the area of triangle ABC?\nChoices:\nA: 25cm2\nB: 30cm2\nC: 32.5cm2\nD: 35cm2"
... | [
"mulberry_images/geoqa_plus/11875.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194636 | [
{
"from": "user",
"value": "<image>In the illustrated diagram, where O represents the circumcircle of triangle ABC and AB serves as the diameter, if OC and AC both have a magnitude of 5 units, what is the length of BC?\nChoices:\nA: 10\nB: 9\nC: 8\nD: 5√{3}"
},
{
"from": "assistant",
"value": "<... | [
"mulberry_images/geoqa_plus/12695.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194637 | [
{
"from": "user",
"value": "<image>If the diagram illustrates a method for measuring the width of a river, with BD measuring 150m, DC measuring 75m, and EC measuring 60m, what would be the length of AB?\nChoices:\nA: 60m\nB: 80m\nC: 100m\nD: 120m"
},
{
"from": "assistant",
"value": "<think> Okay... | [
"mulberry_images/geoqa_plus/12549.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194638 | [
{
"from": "user",
"value": "<image>Looking at the diagram, we can see that the line DE passes through point A and is parallel to BC. With angle B measuring 45° and angle 1 measuring 65°, what would be the measure of angle 2?\nChoices:\nA: 65°\nB: 70°\nC: 75°\nD: 80°"
},
{
"from": "assistant",
"v... | [
"mulberry_images/geoqa_plus/11149.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194639 | [
{
"from": "user",
"value": "<image>In the given diagram, triangle ABC is depicted with BD as the median. The midpoints of BD and CE are point E and point F, respectively. If the area of triangle ABC is 12, what is the area of triangle AEF?\nChoices:\nA: 2\nB: 3\nC: 4\nD: 6"
},
{
"from": "assistant",... | [
"mulberry_images/geoqa_plus/11972.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194640 | [
{
"from": "user",
"value": "<image>In triangle ABC, depicted in the figure, angle BAC is bisected by AD. Line DE is parallel to AC, while the lengths of AB and BD are 7cm and 3cm, respectively. Calculate the perimeter of triangle BDE.\nChoices:\nA: 13cm\nB: 10cm\nC: 4cm\nD: 7cm"
},
{
"from": "assist... | [
"mulberry_images/geoqa_plus/12480.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194641 | [
{
"from": "user",
"value": "<image>Within the given figure, quadrilateral ABCD is a rhombus where the diagonals AC and BD intersect at point O. Point E is located on side AD and serves as the midpoint. Perpendiculars EF and EG are drawn, with EF passing through point E and being perpendicular to BD, and EG ... | [
"mulberry_images/geoqa_plus/12734.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194642 | [
{
"from": "user",
"value": "<image>Given that the diagonals AC and BD intersect at point O in diamond ABCD, with BD measuring 6 units and AC measuring 8 units, what is the total perimeter of the diamond?\nChoices:\nA: 40\nB: 20\nC: 10\nD: 5"
},
{
"from": "assistant",
"value": "<think> Okay, let'... | [
"mulberry_images/geoqa_plus/12803.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194643 | [
{
"from": "user",
"value": "<image>Given a circle O with a radius of 2, let C be a point on the extension of diameter AB. If CD is tangent to the circle at point D and angle DAC measures 30 degrees, what is the length of the segment CD?\nChoices:\nA: 1\nB: √{3}\nC: 2\nD: 2√{3}"
},
{
"from": "assista... | [
"mulberry_images/geoqa_plus/12625.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194644 | [
{
"from": "user",
"value": "<image>In the given diagram, rectangle ABCD is depicted with diagonals AC and BD intersecting at point O. A point P is allowed to move along side AD. From point P, perpendiculars PE and PF are drawn to AC and BD respectively. If the lengths of AB and BC are 6 and 8 units respecti... | [
"mulberry_images/geoqa_plus/12767.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194645 | [
{
"from": "user",
"value": "<image>Consider the figure showing triangle ABC with an inscribed circle O. The tangents to this circle at vertices D, E, and F are represented by AB, BC, and CA respectively. If AD measures 2.0 units and BC measures 5.0 units, what is the perimeter of triangle ABC?\nChoices:\nA:... | [
"mulberry_images/geoqa_plus/1249.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194646 | [
{
"from": "user",
"value": "<image>What is the measure of angle C in the given figure, where points A, B, and C are all on circle O and the degree of arc ACB is 300 degrees?\nChoices:\nA: 30°\nB: 40°\nC: 50°\nD: 60°"
},
{
"from": "assistant",
"value": "<think> Okay, let's see. The problem displa... | [
"mulberry_images/geoqa_plus/1745.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194647 | [
{
"from": "user",
"value": "<image>Given the figure illustrating parallelogram ABCD, where point O is the intersection of AC and BD, and line OE, perpendicular to AC, intersects side AD at point E, if the perimeter of triangle CDE is 11cm, what is the perimeter of parallelogram ABCD?\nChoices:\nA: 20cm\nB: ... | [
"mulberry_images/geoqa_plus/12523.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194648 | [
{
"from": "user",
"value": "<image>In the figure provided, l1, l2, and l3 are parallel lines. Given that angle 1 is 60° and angle 2 is 20°, what is the measure of angle 3? \nChoices:\nA: 120°\nB: 140°\nC: 110°\nD: 130°"
},
{
"from": "assistant",
"value": "<think> Okay, let's see. So there are th... | [
"mulberry_images/geoqa_plus/10967.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194649 | [
{
"from": "user",
"value": "<image>If OC and OD are the angle bisectors for angle AOB and angle BOC respectively, and the measure of angle AOB is 120.0 degrees, what is the measure of angle AOD?\nChoices:\nA: 30°\nB: 60°\nC: 50°\nD: 90°"
},
{
"from": "assistant",
"value": "<think> Okay, let's ta... | [
"mulberry_images/geoqa_plus/1261.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194650 | [
{
"from": "user",
"value": "<image>Given a rectangle ABCD with diagonals AC and BD intersecting at point O, if point M is the midpoint of side AB and OM measures 4 units while AB measures 6 units, what would be the length of BD?\nChoices:\nA: 4\nB: 5\nC: 8\nD: 10"
},
{
"from": "assistant",
"valu... | [
"mulberry_images/geoqa_plus/12952.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194651 | [
{
"from": "user",
"value": "<image>In the given picture, points A and B are situated at opposite ends of a pond, and Xiao Ming intends to determine the distance between them using a rope. However, the rope falls short, prompting a classmate to suggest a method involving locating a point C on the ground reac... | [
"mulberry_images/geoqa_plus/13036.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194652 | [
{
"from": "user",
"value": "<image>In quadrilateral ABCD, where AB is smaller than BC and the perpendicular bisector of diagonal AC intersects AD at point E, if the perimeter of ABCD is 20cm, what is the perimeter of triangle CDE?\nChoices:\nA: 20cm\nB: 40cm\nC: 15cm\nD: 10cm"
},
{
"from": "assistan... | [
"mulberry_images/geoqa_plus/12442.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194653 | [
{
"from": "user",
"value": "<image>As shown in the diagram, pentagon ABCDE is inscribed within circle O. If angle CAD is 40 degrees, what is the degree measure of angle B plus angle E?\nChoices:\nA: 200°\nB: 215°\nC: 230°\nD: 220°"
},
{
"from": "assistant",
"value": "<think> Okay, let's see. The... | [
"mulberry_images/geoqa_plus/11290.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194654 | [
{
"from": "user",
"value": "<image>When trying to estimate the distance between points A and B on both sides of the pond, we select point C on one side. Obtaining the midpoints D and E of AC and BC and finding DE to be 15m, what is the measure of the distance between points A and B?\nChoices:\nA: 15m\nB: 20... | [
"mulberry_images/geoqa_plus/12958.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194655 | [
{
"from": "user",
"value": "<image>What is the perimeter of quadrilateral ABED if in the figure of trapezoid ABCD, 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, with DE connecting them?\nChoices:\nA: 17\nB:... | [
"mulberry_images/geoqa_plus/12874.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194656 | [
{
"from": "user",
"value": "<image>In the given figure of triangle ABC, where angle ACB is 90° and angle A is 25°, point D lies on side AB. If the triangle is folded along CD, causing point B to coincide with point B' on side AC, what is the degree measure of angle ADB'?\nChoices:\nA: 25°\nB: 30°\nC: 35°\nD... | [
"mulberry_images/geoqa_plus/11334.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194657 | [
{
"from": "user",
"value": "<image>Given that AB is equal to AC in triangle ABC, AD bisects angle BAC, E is the midpoint of AC, and DE measures 3, determine the length of AB.\nChoices:\nA: 4\nB: 5\nC: 5.5\nD: 6"
},
{
"from": "assistant",
"value": "<think> Okay, so we have an isosceles triangle A... | [
"mulberry_images/geoqa_plus/12866.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194658 | [
{
"from": "user",
"value": "<image>Given that a right triangle is positioned across the opposing edges of a ruler, with vertex angles equal to 45.0 degrees, and angle 2 is established at 60.0 degrees, what is the value of angle 1?\nChoices:\nA: 10°\nB: 15°\nC: 20°\nD: 25°"
},
{
"from": "assistant",
... | [
"mulberry_images/geoqa_plus/1190.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194659 | [
{
"from": "user",
"value": "<image>In the given 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, so I have this ... | [
"mulberry_images/geoqa_plus/12870.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194660 | [
{
"from": "user",
"value": "<image>In the provided diagram, triangle ABC has AD as its median and E is the midpoint of AD. If the area of triangle ABC is known to be 12, what is the exact area of triangle ABE?\nChoices:\nA: 2\nB: 3\nC: 4\nD: 6"
},
{
"from": "assistant",
"value": "<think> Okay, l... | [
"mulberry_images/geoqa_plus/11865.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194661 | [
{
"from": "user",
"value": "<image>The figure illustrates triangle ABC, with points D and E positioned on the line segments AB and AC and the intersection of BE and CD at point F. If angle A equals 60°, angle ACD equals 40°, and angle ABE equals 30°, what is the value of angle CFE?\nChoices:\nA: 50°\nB: 60°... | [
"mulberry_images/geoqa_plus/11413.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194662 | [
{
"from": "user",
"value": "<image>In the given figure, with AB and CD being parallel and the degree measure of angle 2 equal to 125.0, what is the value of angle 1?\nChoices:\nA: 75°\nB: 65°\nC: 55°\nD: 45°"
},
{
"from": "assistant",
"value": "<think> Okay, let's see. The problem shows there ar... | [
"mulberry_images/geoqa_plus/1275.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194663 | [
{
"from": "user",
"value": "<image>In the given figure, a closed curved shape called a \"cam\" is created by drawing arcs with the three vertices of an equilateral triangle as the centers and the side length of the equilateral triangle as the radius. If the side length of the equilateral triangle is 2, what... | [
"mulberry_images/geoqa_plus/12715.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194664 | [
{
"from": "user",
"value": "<image>Triangle ABC is depicted in the figure, where AD serves as the median of side BC. E and F represent the midpoints of AD and BE respectively. If the area of triangle BFD has been determined as 1, what is the area of triangle ABC?\nChoices:\nA: 3\nB: 8\nC: 4\nD: 6"
},
{
... | [
"mulberry_images/geoqa_plus/12015.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194665 | [
{
"from": "user",
"value": "<image>In the provided diagram, it is known that AB is equal to AC and measures 10 units, BC measures 6 units. Arcs with lengths greater than half of AB are drawn using A and B as centers, resulting in the intersection of these arcs at points M and N. Line MN intersects line AC a... | [
"mulberry_images/geoqa_plus/12516.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194666 | [
{
"from": "user",
"value": "<image>If triangle ABC is depicted in the figure, where points D and E lie on the sides AB and AC respectively, such that DE is parallel to BC, and point F is located on the extended line of BC, then angle ACF is measured at 140.0 degrees and angle ADE is measured at 105.0 degree... | [
"mulberry_images/geoqa_plus/1543.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194667 | [
{
"from": "user",
"value": "<image>Given that triangle ABC is represented in the figure, where BD is defined as the median and E and F are respectively the midpoints of segments BD and CE, if the area of triangle AEF is determined to be 3 square centimeters, what is the total area of triangle ABC?\nChoices:... | [
"mulberry_images/geoqa_plus/11803.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194668 | [
{
"from": "user",
"value": "<image>Given the diagram with triangle PBC, where the area of triangle PBC is 15 cm^2 and PB acts as the angle bisector of angle ABC, what is the area of triangle ABC if AP is created perpendicular to BP at point P? \nChoices:\nA: 25cm2\nB: 30cm2\nC: 32.5cm2\nD: 35cm2"
},
{
... | [
"mulberry_images/geoqa_plus/11987.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194669 | [
{
"from": "user",
"value": "<image>Given triangle ABC with side lengths AB=7, AC=6, and BC=5, and the midpoints D and E of AB and AC respectively, what is the value of DE?\nChoices:\nA: 4\nB: 3.5\nC: 3\nD: 2.5"
},
{
"from": "assistant",
"value": "<think> Okay, let's see. We have triangle ABC wit... | [
"mulberry_images/geoqa_plus/12129.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194670 | [
{
"from": "user",
"value": "<image>Given the figure showing quadrilateral ABCD in the shape of a diamond, with its diagonals AC and BD intersecting at point O, and having E as the midpoint of side AD, what would be the perimeter of diamond ABCD if the length of OE is known to be 3.5 units?\nChoices:\nA: 14\... | [
"mulberry_images/geoqa_plus/12072.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194671 | [
{
"from": "user",
"value": "<image>In the diagram of rectangle ABCD, where diagonal AC and BD intersect at point O, if AE is both perpendicular and bisecting BO with a measurement of 2√3, what is the value of OD?\nChoices:\nA: 2cm\nB: 3cm\nC: 4cm\nD: 6cm"
},
{
"from": "assistant",
"value": "<thi... | [
"mulberry_images/geoqa_plus/12786.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194672 | [
{
"from": "user",
"value": "<image>Determine the length of EF when the area of square ABCD is 8 and the area of rhombus AECF is 4.\nChoices:\nA: 4\nB: √{5}\nC: 2\nD: 1"
},
{
"from": "assistant",
"value": "<think> Okay, let's try to figure out the length of EF in the square ABCD. The square has a... | [
"mulberry_images/geoqa_plus/12829.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194673 | [
{
"from": "user",
"value": "<image>Consider the figure showing a cylinder with a height of 8.0 units and a bottom surface with a perimeter of 30.0 units. If ants are crawling on the surface, what is the shortest distance one needs to travel from point A to point B?\nChoices:\nA: 15cm\nB: 17cm\nC: 18cm\nD: 3... | [
"mulberry_images/geoqa_plus/1270.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194674 | [
{
"from": "user",
"value": "<image>In the given diagram of quadrilateral ABCD, the diagonal AC intersects with BD at point O, and AB is perpendicular to AC. With AB measuring 4 units and AC measuring 6 units, what is the length of BD?\nChoices:\nA: 11\nB: 10\nC: 9\nD: 8"
},
{
"from": "assistant",
... | [
"mulberry_images/geoqa_plus/12450.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194675 | [
{
"from": "user",
"value": "<image>Given triangle ABC with a 90-degree angle at B and side lengths AB = 12 units and BC = 5 units, point D moves along side AC. At point E, DE is perpendicular to AB, and at point F, DF is perpendicular to BC. What is the minimum length of EF?\nChoices:\nA: 4.8\nB: \\frac{60}... | [
"mulberry_images/geoqa_plus/12544.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194676 | [
{
"from": "user",
"value": "<image>With reference to the figure given, showing a right angle, if one of the edges of a ruler passes through a vertex of the right angle and the other edge intersects one of the edges of the right angle, what is the measure of angle 2, given that angle 1 is 30.0 degrees?\nChoi... | [
"mulberry_images/geoqa_plus/1446.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194677 | [
{
"from": "user",
"value": "<image>The figure shows diamond ABCD, where the diagonals AC and BD intersect at point O. If BD measures 6 units and AC measures 8 units, what is the perimeter of the diamond?\nChoices:\nA: 40\nB: 20\nC: 10\nD: 5"
},
{
"from": "assistant",
"value": "<think> Okay, so I... | [
"mulberry_images/geoqa_plus/12803.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194678 | [
{
"from": "user",
"value": "<image>Consider the figure provided, where Xiao Ming wants to determine the distance between points A and B along the side of a pond. To facilitate this measurement, Xiao Ming chooses point O on one side of the pond. Afterward, he discovers that the midpoint of OA is point C and ... | [
"mulberry_images/geoqa_plus/12971.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194679 | [
{
"from": "user",
"value": "<image>What is the length of side BC in rectangle ABCD if angle AOB measures 60°, AB is equal to 2, and the two diagonals intersect at point O?\nChoices:\nA: 2\nB: 4\nC: 2√{3}\nD: 4√{3}"
},
{
"from": "assistant",
"value": "<think> Okay, so I have this rectangle ABCD w... | [
"mulberry_images/geoqa_plus/12870.png"
] | vision_r1_mulberry_sft_full |
vision_r1_mulberry_sft_full-194680 | [
{
"from": "user",
"value": "<image>Given the figure displaying rectangle ABCD, where the diagonals intersect at point O and angle AOB is measured at 60 degrees, if the length of AC is 8 units, what is the length of AB?\nChoices:\nA: 4\nB: 5\nC: 6\nD: 8"
},
{
"from": "assistant",
"value": "<think... | [
"mulberry_images/geoqa_plus/12116.png"
] | vision_r1_mulberry_sft_full |
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