id stringlengths 4 8 | image_url stringlengths 77 81 | query stringlengths 7 1.32k | answer stringlengths 1 148 | choice stringlengths 4 597 | question_type stringclasses 2
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geo409 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/409.png | In rectangle ABCD, AB=16. As shown in the figure, a sector ABE is cut out and formed into a cone (with AB and AE coinciding). What is the radius of the base of this cone? | A | ['4', '16', '4√{2}', '8'] | multi_choice |
geo410 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/410.png | A large sunshade umbrella can be approximately considered as a conical shape when its surface is opened, as shown in the figure. The slant height is 2.5 meters, and the radius of the base is 2 meters. What is the surface area of the umbrella? | B | ['\\frac{25}{4}平方米', '5π平方米', '10π平方米', '\\frac{15}{4}π平方米'] | multi_choice |
geo411 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/411.png | A sector of paper with a central angle of 120° and a radius of 6 cm is rolled into a bottomless conical paper hat (as shown in the figure). What is the height of this paper hat? | C | ['2cm', '3√{2}cm', '4√{2}cm', '4cm'] | multi_choice |
geo412 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/412.png | As shown in the figure, the radius of the base of the cone, OA, is 2, and the slant height, AB, is 3. What is the lateral surface area of this cone? | B | ['3π', '6π', '12π', '18π'] | multi_choice |
geo413 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/413.png | As shown in the figure, the radius of the base of the conical chimney is 15 cm, and the slant height is 20 cm. The minimum area of the iron sheet required to make such a chimney cap is () | B | ['1500πcm^{2}', '300πcm^{2}', '600πcm^{2}', '150πcm^{2}'] | multi_choice |
geo414 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/414.png | As shown in the figure, in the right triangle ABC, ∠C=90°, AB=5, AC=4. If the right triangle ABC is rotated around the line where side AC lies, what is the total surface area of the resulting solid? | C | ['15π', '20π', '24π', '36π'] | multi_choice |
geo415 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/415.png | As shown in the figure, an open umbrella can be approximately regarded as a cone. The diameter AC of the circle where the ends of the umbrella ribs (the frame under the fabric that can support the fabric) are located is 12 decimeters, and the length of the umbrella rib AB is 9 decimeters. How much silk fabric is needed to make such an umbrella, at least in square decimeters? | B | ['36π', '54π', '27π', '128π'] | multi_choice |
geo416 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/416.png | As shown in the figure, the slant height of a conical ice cream cone is 13 cm, and the height is 12 cm. What is the area of the base of the cone? | B | ['10πcm^{2}', '25πcm^{2}', '60πcm^{2}', '65πcm^{2}'] | multi_choice |
geo417 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/417.png | As shown in the figure, in the right triangle ABC, ∠BAC=90°, AC=4, and BC=5. If the right triangle ABC is rotated around the line AC for one full turn, what is the lateral surface area of the resulting cone? | C | ['9π', '12π', '15π', '20π'] | multi_choice |
geo418 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/418.png | As shown in the figure: The lateral surface of a cone is unfolded into a semicircle with a radius of 2. What is the radius of the base of the cone? | A | ['1', '2', '\\frac{1}{2}', '4'] | multi_choice |
geo419 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/419.png | As shown in the figure, a sector-shaped piece of paper with a radius of 15 cm is used to form a conical paper tube (with no gaps or overlaps at the joint). The radius of the base of the conical paper tube is 6 cm. What is the area of the sector in cm²? | B | ['90', '90π', '180π', '126π'] | multi_choice |
geo420 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/420.png | As shown in the figure, the lower part of the ice cream cone is conical, with the diameter of the base circle being 5 cm and the slant height being 8 cm. What is the area of the wrapping paper for the conical part of the cone (ignoring the seam)? | B | ['36πcm^{2}', '20πcm^{2}', '18πcm^{2}', '8πcm^{2}'] | multi_choice |
geo421 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/421.png | As shown in the figure, Xiaolan made a conical birthday hat using colored paper. If the radius of the base is 5 cm and the slant height is 10 cm, without considering the seam, what is the lateral surface area of this cone? | D | ['250πcm^{2}', '125πcm^{2}', '100πcm^{2}', '50πcm^{2}'] | multi_choice |
geo422 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/422.png | As shown in the figure, given that the diameter of the base of the cone is 6 and the height is 4, what is the length of its slant height? | D | ['3', '4', '\\frac{9}{2}', '5'] | multi_choice |
geo423 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/423.png | As shown in the figure, to measure the height of the school flagpole, Xiao Dong uses a 3.2m long bamboo pole as a measuring tool. He moves the bamboo pole so that the shadows of both the bamboo pole and the flagpole fall exactly at the same point A on the ground. At this moment, the bamboo pole is 8m away from point A and 22m away from the flagpole. What is the height of the flagpole? | C | ['6m', '8.8m', '12m', '30m'] | multi_choice |
geo424 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/424.png | As shown in the figure, in order to measure the height of a tree, Xiao Ming uses a 2-meter-long bamboo pole as a measuring tool. He moves the bamboo pole so that the shadow of the top of the pole and the shadow of the top of the tree fall exactly at the same point on the ground. At this moment, the bamboo pole is 5 meters away from this point, and the tree is 10 meters away from this point. What is the height of the tree? | B | ['5m', '6m', '7m', '8m'] | multi_choice |
geo425 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/425.png | As shown in the figure, the street lamp on the utility pole is 8 meters above the ground. Xiao Ming (AB), who is 1.6 meters tall, stands at point A, which is 20 meters away from the base of the utility pole (point O). What is the length of Xiao Ming's shadow AM? | B | ['4米', '5米', '6米', '8米'] | multi_choice |
geo426 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/426.png | As shown in the figure, use the benchmark BE to measure the height of the building. The height of the benchmark BE is 1.5m, AB is measured to be 2m, and BC is 14m. What is the height of the building CD in meters? | B | ['10.5', '12', '13', '15'] | multi_choice |
geo427 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/427.png | As shown in the figure, points A and B are located at the two ends of a pond. Xiao Ming wants to measure the distance between A and B using a rope, but the rope is not long enough. So he came up with a method: first, he selects a point O on the ground that can directly reach points A and B. He connects AO and extends it to C, making OC = 1/2 AO. He then connects BO and extends it to D, making OD = 1/2 OB. He connects DC and measures DC to be 20 meters. In this way, Xiao Ming can calculate the distance between A and B as () | B | ['30m', '40m', '60m', '80m'] | multi_choice |
geo428 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/428.png | As shown in the figure, to estimate the width of the river, a target point A is selected on the opposite bank of the river. Points B, C, D, and E are taken on the near bank such that points A, B, and D are on a straight line, and AD is perpendicular to DE. Points A, C, and E are also on a straight line, and DE is parallel to BC. If BC = 24m, BD = 12m, and DE = 40m, then the width of the river AB is approximately () | B | ['20m', '18m', '28m', '30m'] | multi_choice |
geo429 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/429.png | As shown in the figure, points A, B, and C are on circle O. If ∠C = 44°, then what is the measure of ∠AOB? | B | ['22°', '88°', '66°', '70°'] | multi_choice |
geo430 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/430.png | As shown in the figure, Xiao Liu made a schematic diagram of a kite frame. It is known that BC∥PQ, AB:AP=2:5, and BC=20cm. What is the length of PQ? | B | ['45cm', '50cm', '60cm', '80cm'] | multi_choice |
geo431 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/431.png | As shown in the figure, use the benchmark BE to measure the height of the building DC. If the length of the benchmark BE is 1.5 meters, AB is measured to be 2 meters, BC is 8 meters, and points A, E, and D are on a straight line, then the height of the building CD is () | D | ['9.5米', '9米', '8米', '7.5米'] | multi_choice |
geo432 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/432.png | As shown in the figure, Xiaoying from the math interest group wants to measure the height of a tree in front of the teaching building. During the afternoon extracurricular activity, she measured the shadow length of a 1m long bamboo pole to be 0.8m. However, when she immediately measured the tree height, she found that part of the tree's shadow did not fall on the ground but on the wall of the teaching building (as shown in the figure). She first measured the shadow height on the wall to be 1.2m and then measured the shadow length on the ground to be 2.6m. Please help her calculate the height of the tree. | C | ['3.25m', '4.25m', '4.45m', '4.75m'] | multi_choice |
geo433 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/433.png | As shown in the figure, a student with a height of 1.6 meters wants to measure the height of a big tree. She walks from point B to point A along the tree's shadow BA. When she reaches point C, the top of her shadow coincides with the top of the tree's shadow. It is measured that BA = 4 meters and CA = 0.8 meters. What is the height of the tree? | C | ['4.8m', '6.4m', '8m', '10m'] | multi_choice |
geo434 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/434.png | As shown in the figure, in order to measure the height of a certain tree, Xiao Ming uses a 2-meter-long bamboo pole as a measuring tool. He moves the bamboo pole so that the shadow of the top of the bamboo pole and the top of the tree fall exactly at the same point on the ground. At this time, the bamboo pole is 6 meters away from this point, and the tree is 15 meters away from this point. What is the height of the tree? | C | ['4m', '5m', '7m', '9m'] | multi_choice |
geo435 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/435.png | As shown in the figure, point A is on circle O, and BC is a chord of circle O. If ∠A = 50°, what is the measure of ∠OBC? | A | ['40°', '50°', '25°', '100°'] | multi_choice |
geo436 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/436.png | As shown in the figure, two adjacent poles are fixed to the ground with steel cables. One pole's steel cable is tied at a point 4 meters above the ground, and the other pole's steel cable is tied at a point 6 meters above the ground. At what height above the ground does the point P, where the two steel cables intersect, lie? | A | ['2.4m', '2.6m', '2.8m', '3m'] | multi_choice |
geo437 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/437.png | As shown in the figure, on a summer day, Xiao Ling, who is 1.6 meters tall, wants to measure the height of the big tree in front of her house. She walks along the tree's shadow from point B to point A. When she reaches point C, the top of her shadow coincides with the top of the tree's shadow. It is measured that BC = 3.2 meters and CA = 0.8 meters. Therefore, the height of the tree is () | A | ['8m', '6.4m', '4.8m', '10m'] | multi_choice |
geo438 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/438.png | As shown in the figure, it is the left view of a folding small stool. There are two isosceles triangle frames in the figure. One of the isosceles triangle frames has a leg length of 4 and a base length of 6. The other isosceles triangle frame has a leg length of 2. What is the corresponding base length? | D | ['6', '5', '4', '3'] | multi_choice |
geo439 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/439.png | As shown in the figure, Xiao Ming designed a schematic diagram to measure the height of an ancient city wall CD using light. If the distance between the mirror P and the ancient city wall is PD=12 meters, the distance between the mirror P and Xiao Ming is BP=1.5 meters, and Xiao Ming just sees the top point C of the ancient city wall from the mirror. The height of Xiao Ming's eyes from the ground is AB=1.2 meters. What is the height of the ancient city wall? | A | ['9.6米', '18米', '8米', '24米'] | multi_choice |
geo440 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/440.png | As shown in the figure, in order to measure the height of the oil surface inside the oil barrel, a thin wooden stick is inserted into the barrel through a small hole. The length of the inserted part AB of the wooden stick is measured to be 100 cm, and the length of the part DB stained with oil is 60 cm. The height of the barrel AC is 80 cm. What is the height of the oil surface CE inside the barrel in cm? | D | ['60', '32', '50', '48'] | multi_choice |
geo441 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/441.png | As shown in the figure, AB is the diameter of circle O, point C is on circle O, and ∠A = 40°. What is the degree of ∠B? | B | ['65°', '50°', '130°', '80°'] | multi_choice |
geo442 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/442.png | As shown in the figure, the short arm of the railway crossing gate is 1 meter long, and the long arm is 16 meters long. When the end of the short arm drops by 0.5 meters, the end of the long arm rises by how many meters? | C | ['11.25米', '6.6米', '8米', '10.5米'] | multi_choice |
geo443 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/443.png | There is an eye chart with a test distance of 5 meters (as shown in the figure). Based on this eye chart, Xiaohua wants to create an eye chart with a test distance of 3 meters. What is the value in the figure? | D | ['\\frac{3}{2}', '\\frac{2}{3}', '\\frac{3}{5}', '\\frac{5}{3}'] | multi_choice |
geo444 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/444.png | As shown in the figure, Wang Hua places a plane mirror E on the ground to measure the height of the iron tower AB. The distance between the mirror and the iron tower is EB=20 meters, and the distance between the mirror and Wang Hua is ED=2 meters. When Wang Hua sees the top point A of the iron tower from the mirror, it is known that the height of Wang Hua's eyes from the ground is CD=1.5 meters. What is the height of the iron tower AB? | A | ['15米', '米', '16米', '16.5米'] | multi_choice |
geo445 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/445.png | As shown in the figure, in order to measure the width DE of a pond, a point C is found on the shore, and it is measured that CD = 30m. A point A is found on the extension line of DC, and it is measured that AC = 5m. Through point A, AB is drawn parallel to DE, intersecting the extension line of EC at B, and it is measured that AB = 6m. What is the width DE of the pond? | C | ['25m', '30m', '36m', '40m'] | multi_choice |
geo446 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/446.png | As shown in the figure, points A, B, C, D, and E are all on circle O. Arc AB is equal to arc CD, and arc BC is equal to arc DE. If angle D is 128°, then the measure of angle B is () | A | ['128°', '126°', '118°', '116°'] | multi_choice |
geo447 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/447.png | As shown in the diagram, it is a schematic of using a lever to pry a stone. C is the fulcrum. When force is applied to the A end of the lever, the lever rotates around point C, causing the other end B to lift up, and the stone is pried. Now, there is a stone that needs to be rolled. The B end of the lever must be lifted up by 10 cm. Given that the ratio of the lever's effort arm AC to the resistance arm BC is 5:1, to make the stone roll, how much must the A end of the lever be pressed down? | C | ['100cm', '60cm', '50cm', '10cm'] | multi_choice |
geo448 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/448.png | As shown in the figure, the short arm of the railway crossing barrier is 1.25 meters long, and the long arm is 16.5 meters long. When the end of the short arm drops by 0.85 meters, the end of the long arm rises by (ignoring the width of the barrier). | B | ['11米', '11.22米', '17米', '10米'] | multi_choice |
geo449 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/449.png | A student wants to measure the height of the school flagpole using the length of its shadow. As shown in the diagram, at a certain moment, he measures the shadow of a 1-meter long rod to be 1.2 meters. At the same time, the flagpole's shadow is partly on the ground and partly on the wall of a building, with measured lengths of 9.6 meters and 2 meters respectively. What is the height of the school flagpole in meters? | D | ['2', '11.6', '1.2', '10'] | multi_choice |
geo450 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/450.png | One day, Dad took Xiao Ming to a construction site to play. They saw an A-frame structure as shown in the picture. Dad said, 'Xiao Ming, let me test you. The angle ∠1 of this A-frame is 130°. Do you know how much larger ∠3 is compared to ∠2?' Xiao Ming immediately got the correct answer. His answer is () | A | ['50°', '65°', '90°', '130°'] | multi_choice |
geo451 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/451.png | As shown in the figure, △A′B′C′ and △ABC are similar figures with point O as the center of similarity. If the similarity ratio A′O:AO=3:1, and the perimeter of △A′B′C′ is 12, then the perimeter of △ABC is () | A | ['4', '36', '9', '2√{3}'] | multi_choice |
geo452 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/452.png | As shown in the figure, there is a point light source S above a plane mirror. If the reflected light of the point light source is seen at point P, and it is measured that AB=10cm, BC=20cm, PC⊥AC, and PC=24cm, what is the distance from the point light source S to the plane mirror, i.e., the length of SA? | B | ['11cm', '12cm', '13cm', '14cm'] | multi_choice |
geo453 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/453.png | As shown in the figure, in △ABC, ∠C=90°, AB=5, BC=3, what is the value of tanB? | B | ['\\frac{3}{4}', '\\frac{4}{3}', '\\frac{3}{5}', '\\frac{4}{5}'] | multi_choice |
geo454 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/454.png | As shown in the figure, A and D are two points on circle O, and BC is the diameter. If ∠OAC = 55°, what is the degree of ∠D? | A | ['35°', '55°', '65°', '70°'] | multi_choice |
geo455 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/455.png | As shown in the figure, in the right triangle ABC, ∠C=90°, AB=5, BC=3, what is the value of \\cosB? | A | ['\\frac{3}{5}', '\\frac{4}{5}', '\\frac{3}{4}', '\\frac{4}{3}'] | multi_choice |
geo456 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/456.png | As shown in the figure, in △ABC, ∠ACB=90°, CD⊥AB at point D. If CD:AC=2:3, then the value of sin∠BCD is () | B | ['\\frac{2√{5}}{5}', '\\frac{2}{3}', '\\frac{2√{13}}{13}', '\\frac{2}{13}'] | multi_choice |
geo457 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/457.png | As shown in the figure, in circle O, chords AB and CD intersect at point P. If ∠ADC = 20°, then ∠B equals () | A | ['20°', '25°', '30°', '35°'] | multi_choice |
geo458 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/458.png | In right triangle △ABC, ∠C=90°, AB=5, BC=4, then what is \\cosA? | B | ['\\frac{4}{5}', '\\frac{3}{5}', '\\frac{4}{3}', '\\frac{3}{4}'] | multi_choice |
geo459 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/459.png | As shown in the figure, in △ABC, ∠B=90°, AB=3, BC=4, then \\cosA equals () | D | ['\\frac{3}{4}', '\\frac{4}{3}', '\\frac{4}{5}', '\\frac{3}{5}'] | multi_choice |
geo460 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/460.png | As shown in the figure, point A(t, 3) is in the first quadrant, and the acute angle between OA and the x-axis is α. Given that tan(α) = 2, what is the value of t? | B | ['1', '1.5', '2', '3'] | multi_choice |
geo461 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/461.png | As shown in the figure, in the right triangle ABC, ∠C=90°, BC=3, AB=4, what is the value of cosB? | C | ['\\frac{√{7}}{3}', '\\frac{√{7}}{4}', '\\frac{3}{4}', '\\frac{4}{3}'] | multi_choice |
geo462 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/462.png | As shown in the figure, C and D are two points on the circle ⊙O with diameter AB. If ∠ADC = 70°, then ∠CAB = () | B | ['10°', '20°', '30°', '40°'] | multi_choice |
geo463 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/463.png | Place a set of (30°60°90°) and (45°45°90°) triangles as shown in the figure. What is the angle α in the overlapping area? | A | ['105°', '90°', '75°', '60°'] | multi_choice |
geo464 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/464.png | In right triangle ABC, ∠C=90°, AB=6, sinA= rac{2}{3}, then the length of AC is () | B | ['4', '2√{5}', '\\frac{18√{13}}{13}', '\\frac{13√{13}}{12}'] | multi_choice |
geo465 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/465.png | As shown in the figure, in △ABC, ∠C=90°, AB=5, BC=3, CA=4, what is sinA equal to? | C | ['\\frac{3}{4}', '\\frac{4}{3}', '\\frac{3}{5}', '\\frac{4}{5}'] | multi_choice |
geo466 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/466.png | As shown in the figure, in the right triangle ABC, ∠ACB=90°, BC=3, AC=4, what is the value of sinA? | A | ['\\frac{3}{5}', '\\frac{4}{5}', '\\frac{3}{4}', '\\frac{4}{3}'] | multi_choice |
geo467 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/467.png | As shown in the figure, in △ABC, ∠A=90°, AC=9, sinB=0.6, then AB is equal to () | B | ['10', '12', '15', '18'] | multi_choice |
geo468 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/468.png | As shown in the figure, in △ABC, ∠C=90°, AC=2, BC=1, what is the value of cosB? | C | ['\\frac{1}{2}', '\\frac{√{3}}{2}', '\\frac{√{5}}{5}', '\\frac{2√{5}}{5}'] | multi_choice |
geo469 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/469.png | Given that in right triangle ABC, ∠C=90°, BC=12, AC=5, what is the value of cosA? | C | ['\\frac{5}{12}', '\\frac{12}{5}', '\\frac{5}{13}', '\\frac{12}{13}'] | multi_choice |
geo470 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/470.png | As shown in the figure, points A, B, and C are all on circle O. If ∠ACB = 48°, then what is the measure of ∠AOB? | A | ['96°', '48°', '42°', '24°'] | multi_choice |
geo471 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/471.png | As shown in the figure, in △ABC, ∠C=90°, AC=4, BC=3, then sinA=() | A | ['\\frac{3}{5}', '\\frac{4}{5}', '\\frac{5}{3}', '\\frac{3}{4}'] | multi_choice |
geo472 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/472.png | Given that in right triangle ABC, ∠C=90°, sinA=\frac{1}{3}, and BC=2, find AB. | A | ['6', '4√{2}', '3', '2√{2}'] | multi_choice |
geo473 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/473.png | As shown in the figure, in △ABC, ∠ACB=90°, ∠A=15°, AB=8, then the value of AC•BC is () | D | ['14', '16√{3}', '4√{15}', '16'] | multi_choice |
geo474 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/474.png | In the semicircle shown in the figure, AD is the diameter, and AD = 3, AC = 2. What is the value of \( \\cos∠B \)? | C | ['\\frac{2}{3}', '\\frac{3}{2}', '\\frac{√{5}}{3}', '\\frac{√{5}}{2}'] | multi_choice |
geo475 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/475.png | As shown in the figure, in △ABC, ∠C=90°, AB=5, AC=3, then sinB=() | C | ['\\frac{3}{4}', '\\frac{4}{3}', '\\frac{3}{5}', '\\frac{4}{5}'] | multi_choice |
geo476 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/476.png | In right triangle △ABC, ∠C=90°, if sinA= rac{3}{5}, then cosB=() | D | ['\\frac{5}{3}', '\\frac{4}{5}', '\\frac{3}{4}', '\\frac{3}{5}'] | multi_choice |
geo477 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/477.png | As shown in the figure, △ABC is inscribed in circle O, and AC is the diameter of circle O. Given that ∠ACB = 52°, point D is on segment AC. What is the measure of ∠D? | B | ['52°', '38°', '19°', '26°'] | multi_choice |
geo478 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/478.png | As shown in the figure, in the obtuse triangle △ABC, ∠A=30°, what is the value of tanA? | C | ['√{3}', '\\frac{√{3}}{2}', '\\frac{√{3}}{3}', '无法确定'] | multi_choice |
geo479 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/479.png | As shown in the figure, in the Cartesian coordinate system, the coordinates of point A are (4, 3). What is the value of tanα? | D | ['\\frac{4}{5}', '\\frac{3}{5}', '\\frac{4}{3}', '\\frac{3}{4}'] | multi_choice |
geo480 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/480.png | As shown in the figure, in the right triangle BAD, extend the hypotenuse BD to point C, making DC = \frac{1}{2}BD. Connect AC. If tanB = \frac{5}{3}, then the value of tan∠CAD is () | D | ['\\frac{√{3}}{3}', '\\frac{√{3}}{5}', '\\frac{1}{3}', '\\frac{1}{5}'] | multi_choice |
geo481 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/481.png | As shown in the figure, in circle O, arc AB = arc AC, ∠A = 36°, then the degree of ∠C is () | D | ['44°', '54°', '62°', '72°'] | multi_choice |
geo482 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/482.png | As shown in the figure, points A, B, C, and D are all on circle O. OB is perpendicular to CD, and ∠BOC = 50°. What is the measure of ∠BAD? | D | ['50°', '40°', '30°', '25°'] | multi_choice |
geo483 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/483.png | As shown in the figure, point A is on the circle O with a radius of 2. BC is a chord of circle O, and OD is perpendicular to BC at D. If ∠BAC = 60°, what is the length of OD? | C | ['2', '√{3}', '1', '\\frac{√{3}}{2}'] | multi_choice |
geo484 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/484.png | As shown in the figure, the radius of circle O is 5, AB is a chord, and point C is the midpoint of AB. If ∠ABC = 30°, then the length of chord AB is () | D | ['\\frac{1}{2}', '5', '\\frac{5√{3}}{2}', '5√{3}'] | multi_choice |
geo485 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/485.png | As shown in the figure, AB is the diameter of the semicircle ⊙O. The sides AC and BC of △ABC intersect the semicircle at D and E respectively, and E is the midpoint of BC. Given that ∠BAC = 50°, find ∠C. | C | ['55°', '60°', '65°', '70°'] | multi_choice |
geo486 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/486.png | As shown in the figure, AB is a chord of circle O, OA and OC are radii of circle O, AC = BC, and ∠BAO = 37°. What is the measure of ∠AOC in degrees? | D | ['74', '106', '117', '127'] | multi_choice |
geo487 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/487.png | As shown in the figure, AB is the diameter of circle O, C is a point on circle O, OD is perpendicular to BC at point D, and AC = 8. What is the length of OD? | B | ['3', '4', '4.5', '5'] | multi_choice |
geo488 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/488.png | As shown in the figure, the radius of circle O is 6. Points A, B, and C are on circle O, and ∠BCA = 45°. What is the distance from point O to chord AB? | C | ['3', '6', '3√{2}', '6√{2}'] | multi_choice |
geo489 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/489.png | As shown in the figure, the central angle ∠AOB = 60°, then the measure of the inscribed angle ∠ACB is () | A | ['30°', '60°', '90°', '120°'] | multi_choice |
geo490 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/490.png | As shown in the figure, it is known that AB is a chord of circle O, radius OC is perpendicular to AB, point D is a point on circle O, and point D and point C are located on opposite sides of chord AB. Connect AD, CD, and OB. If ∠BOC = 70°, then ∠ADC = () | B | ['40°', '35°', '30°', '28°'] | multi_choice |
geo491 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/491.png | As shown in the figure, A, B, and C are three points on circle O. If ∠ABO = 30° and ∠ACO = 40°, what is the measure of ∠BOC (less than a straight angle)? | D | ['70°', '100°', '110°', '140°'] | multi_choice |
geo492 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/492.png | As shown in the figure, in circle O, arc AB is equal to arc BC, point D is on circle O, and angle CDB is 20°. What is the measure of angle AOB? | B | ['35°', '40°', '45°', '50°'] | multi_choice |
geo493 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/493.png | Place the right triangle △ABC and the right triangle △CDE on the same horizontal table, arranged as shown in the figure, so that the two right-angle vertices coincide and the two hypotenuses are parallel. If ∠B=25° and ∠D=58°, what is the measure of ∠BCE? | B | ['83°', '57°', '54°', '33°'] | multi_choice |
geo494 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/494.png | As shown in the figure, ⊙O is the circumcircle of △ABC. Given that ∠ACO=30°, what is the measure of ∠B? | C | ['30°', '45°', '60°', '75°'] | multi_choice |
geo495 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/495.png | As shown in the figure, AB is the diameter of circle O, and points C and D are two points on the circle. If ∠AOC = 100°, then what is the measure of ∠D? | D | ['50°', '60°', '45°', '40°'] | multi_choice |
geo496 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/496.png | As shown in the figure, ⊙O is the circumcircle of △ABC, ∠A=40°, then ∠OCB equals () | B | ['60°', '50°', '40°', '30°'] | multi_choice |
geo497 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/497.png | As shown in the figure, AB is the diameter of circle O, and CE is a chord. If ∠AOE = 60°, what is the measure of ∠C? | C | ['30°', '45°', '60°', '120°'] | multi_choice |
geo498 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/498.png | As shown in the figure, chords AB and CD intersect at point P. Given that ∠B = 30° and ∠APD = 80°, what is the measure of ∠A? | C | ['30°', '50°', '70°', '100°'] | multi_choice |
geo499 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/499.png | As shown in the figure, in circle O, the central angle ∠BOC = 100°, then ∠BAC = () | A | ['50°', '60°', '70°', '75°'] | multi_choice |
geo500 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/500.png | As shown in the figure, in circle O, arc AB = arc AC, ∠C = 75°, then the degree of ∠A is () | A | ['30°', '35°', '45°', '60°'] | multi_choice |
geo501 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/501.png | As shown in the figure, in circle O, chord AB is parallel to chord CD. If ∠ABC = 30°, then ∠BOD = () | C | ['40°', '50°', '60°', '70°'] | multi_choice |
geo502 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/502.png | As shown in the figure, the diameter BD of circle O is 2, and ∠A = 60°. What is the length of BC? | A | ['√{3}', '2√{3}', '3√{3}', '4√{3}'] | multi_choice |
geo503 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/503.png | As shown in the figure, in circle O, AB = AC, and ∠ADC = 20°, what is the measure of ∠AOB? | A | ['40°', '30°', '20°', '10°'] | multi_choice |
geo504 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/504.png | As shown in the figure, given: AB is the diameter of circle O, chord CD is perpendicular to AB, connect OC and AD, ∠OCD=32°, then ∠A=() | B | ['32°', '29°', '58°', '45°'] | multi_choice |
geo505 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/505.png | As shown in the figure, line segment AB is the diameter of circle O, chord CD is perpendicular to AB, and ∠CAB = 25°. What is ∠AOD equal to? | C | ['155°', '140°', '130°', '110°'] | multi_choice |
geo506 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/506.png | As shown in the figure, given that points A and B are on circle O, if ∠AOB = 80°, then ∠ACB = () | D | ['80°', '70°', '60°', '40°'] | multi_choice |
geo507 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/507.png | The cross-section of a circular sewer with a diameter of 100 cm is shown in the figure. The width of the water surface is 60 cm. What is the maximum depth of the water in the sewer? | A | ['90cm', '80cm', '60cm', '50cm'] | multi_choice |
geo508 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/508.png | As shown in the figure, AB is the diameter of circle O, and chord CD is perpendicular to AB at point E. Given that ∠CDB = 30° and the radius of circle O is 6, what is the length of the distance OE from the center O to chord CD? | D | ['6', '5', '3√{3}', '3'] | multi_choice |
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