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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geo309 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/309.png | As shown in the figure, place the right-angle vertex of a triangular ruler on one side of a straight ruler. When ∠2 = 38°, what is ∠1? | A | ['52°', '38°', '42°', '60°'] | multi_choice |
geo310 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/310.png | As shown in the figure, AB is the diameter of circle O, and points C and D are on circle O. If ∠C = 20°, then what is the measure of ∠ABD? | B | ['80°', '70°', '50°', '40°'] | multi_choice |
geo311 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/311.png | As shown in the figure, in △ABC, point D is on side AB, point E is on side AC, and DE∥BC. Given ∠B=40°, ∠AED=60°, what is the measure of ∠A? | C | ['100°', '90°', '80°', '70°'] | multi_choice |
geo312 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/312.png | As shown in the figure, in △ABC, ∠A=90°, point D is on side AC, and DE∥BC. If ∠1=35°, then the measure of ∠B is () | C | ['25°', '35°', '55°', '65°'] | multi_choice |
geo313 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/313.png | As shown in the figure, in △ABC, AC = 4 cm, the perpendicular bisector of segment AB intersects AC at point N, and the perimeter of △BCN is 7 cm. What is the length of BC? | C | ['1cm', '2cm', '3cm', '4cm'] | multi_choice |
geo314 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/314.png | As shown in the figure, quadrilateral ABCD is an inscribed quadrilateral of circle O. If ∠DAB = 60°, then the measure of ∠BCD is () | D | ['60°', '90°', '100°', '120°'] | multi_choice |
geo315 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/315.png | As shown in the figure, AB ∥ CD, ∠D = 26°, ∠E = 35°, then what is the degree of ∠ABE? | A | ['61°', '71°', '109°', '119°'] | multi_choice |
geo316 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/316.png | As shown in the figure, points A, B, and C are on circle O, and ∠A = 60°. What is ∠BOC? | C | ['60°', '90°', '120°', '135°'] | multi_choice |
geo317 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/317.png | As shown in the figure, line a is parallel to line b, AB is perpendicular to BC, and ∠1 = 40°. What is the measure of ∠2? | C | ['30°', '40°', '50°', '60°'] | multi_choice |
geo318 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/318.png | As shown in the figure, given that point O is on the line AB, CO is perpendicular to DO at point O, and if ∠1 = 145°, then the measure of ∠3 is () | C | ['35°', '45°', '55°', '65°'] | multi_choice |
geo319 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/319.png | As shown in the figure, △ABE ≌ △ACD, AB = AC, BE = CD, ∠B = 50°, ∠AEC = 120°, then the degree of ∠DAC is equal to () | B | ['120°', '70°', '60°', '50°'] | multi_choice |
geo320 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/320.png | As shown in the figure, 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 bamboo pole and the top of the tree fall exactly at the same point O on the ground. At this moment, the bamboo pole is 6 meters away from ... | C | ['4m', '5m', '7m', '9m'] | multi_choice |
geo321 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/321.png | As shown in the figure, AB ∥ CD, ∠E = 40°, ∠A = 110°, then the degree of ∠C is () | D | ['60°', '80°', '75°', '70°'] | multi_choice |
geo322 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/322.png | As shown in the figure, in circle O, chords AB and CD intersect at point M. Given ∠A = 45° and ∠AMD = 75°, what is the measure of ∠B? | C | ['15°', '25°', '30°', '75°'] | multi_choice |
geo323 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/323.png | As shown in the figure, the line l intersects the circle O with a radius of 5 cm at points A and B, and is perpendicular to the radius OC, with the foot of the perpendicular being H. If AB = 8 cm, to make l tangent to the circle O, l should be translated downward along the line OC by () | B | ['1cm', '2cm', '3cm', '4cm'] | multi_choice |
geo324 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/324.png | As shown in the figure, line a is parallel to line b, and ∠1 = 55°. What is ∠2? | C | ['35°', '45°', '55°', '65°'] | multi_choice |
geo325 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/325.png | As shown in the figure, points A, B, C, and P are on circle O. CD is perpendicular to OA, and CE is perpendicular to OB, with the feet of the perpendiculars being D and E, respectively. Given that ∠DCE = 40°, what is the measure of ∠P? | B | ['140°', '70°', '60°', '40°'] | multi_choice |
geo326 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/326.png | As shown in the figure, AB ∥ CD, AE bisects ∠CAB and intersects CD at point E. If ∠C = 50°, then ∠AED = () | B | ['65°', '115°', '125°', '130°'] | multi_choice |
geo327 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/327.png | As shown in the figure, in △ABC, ∠CAB=70°. Rotate △ABC counterclockwise around point A to the position of △AB'C', making CC'∥AB. What is the degree of ∠BAB'? | C | ['70°', '35°', '40°', '50°'] | multi_choice |
geo328 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/328.png | As shown in the figure, AB is the diameter of circle O, and quadrilateral ABCD is an inscribed quadrilateral of circle O. Point P is on the extension of BA, and PD is tangent to circle O at point D. If ∠BCD = 120°, then what is the measure of ∠APD? | D | ['45°', '40°', '35°', '30°'] | multi_choice |
geo329 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/329.png | As shown in the figure, in △ABC, points D, E, and F are on sides AC, AB, and BC respectively. EF is parallel to AC, and DF is parallel to AB. If ∠B = 45°, ∠C = 65°, then what is the measure of ∠EFD? | B | ['45°', '70°', '80°', '100°'] | multi_choice |
geo330 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/330.png | A ship and a fishing boat depart from port O simultaneously along their respective courses, as shown in the figure. The ship travels 60 nautical miles from port O in the direction of 20° west of north to reach point M. At the same time, the fishing boat has traveled to point N, which is 80 nautical miles away from port... | C | ['50°', '60°', '70°', '80°'] | multi_choice |
geo331 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/331.png | Shaoxing is famous for its bridges. As shown in the figure, the distance from the top of the stone arch bridge to the water surface, CD, is 8 meters, and the radius of the arch, OC, is 5 meters. What is the width of the water surface, AB? | D | ['4m', '5m', '6m', '8m'] | multi_choice |
geo332 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/332.png | As shown in the figure: it is a section of stairs, the height BC is 3m, the hypotenuse AC is 5m. If a carpet is to be laid on the stairs, then at least how much carpet is needed? | C | ['5m', '6m', '7m', '8m'] | multi_choice |
geo333 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/333.png | As shown in the figure, in △ABC, ∠BAC=70°, △ABC is rotated clockwise around point C by a certain angle to obtain △DEC, where point D corresponds to point A, and ED passes through point A. What is the degree of the rotation angle? | C | ['30°', '35°', '40°', '45°'] | multi_choice |
geo334 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/334.png | As shown in the figure, given four lines a, b, c, and d, where a∥b and c∥d, and ∠1=110°, what is the value of ∠2? | B | ['50°', '70°', '90°', '110°'] | multi_choice |
geo335 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/335.png | As shown in the figure, CD is the diameter of circle O. Given that ∠1 = 30°, what is the value of ∠2? | C | ['30°', '45°', '60°', '70°'] | multi_choice |
geo336 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/336.png | As shown in the figure, AB is the diameter of circle O, and CD is a chord of circle O. If ∠BAC = 22°, what is the measure of ∠ADC? | C | ['22°', '58°', '68°', '78°'] | multi_choice |
geo337 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/337.png | As shown in the figure, in △ABC and △ADE, points C and D are on AE and AB respectively. BC and DE intersect at point F. If BD = DC = CE and ∠ADC + ∠ACD = 114°, then what is ∠DFC? | B | ['114°', '123°', '132°', '147°'] | multi_choice |
geo338 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/338.png | As shown in the figure, AB is tangent to circle O at point A, BO intersects circle O at point C, and point D is on the major arc AC. Given that ∠CDA = 27°, what is the measure of ∠B? | C | ['27°', '34°', '36°', '54°'] | multi_choice |
geo339 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/339.png | As shown in the figure, the diagonals of parallelogram ABCD intersect at point O, and AB = 6. The perimeter of △OCD is 16. What is the sum of AC and BD? | C | ['10', '16', '20', '22'] | multi_choice |
geo340 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/340.png | As shown in the figure, place the right-angle vertex of a triangle with a 30° angle on one of two parallel lines. If ∠1 = 35°, then the degree of ∠2 is () | C | ['10°', '20°', '25°', '30°'] | multi_choice |
geo341 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/341.png | As shown in the figure, point O is a point on line AB, and ∠1 = 65°. What is the measure of ∠2? | D | ['25°', '65°', '105°', '115°'] | multi_choice |
geo342 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/342.png | Place a ruler and a set square as shown in the figure. If ∠1 = 46°, what is the degree of ∠2? | A | ['136°', '138°', '140°', '142°'] | multi_choice |
geo343 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/343.png | As shown in the figure, line AB is parallel to line CD, and line EF intersects lines AB and CD at points E and F, respectively. A perpendicular line FG is drawn from point F to line EF, intersecting line AB at point G. If ∠1 = 36°, what is the measure of ∠2? | B | ['36°', '54°', '46°', '40°'] | multi_choice |
geo344 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/344.png | As shown in the figure, in circle O, it is known that ∠OAB = 22.5°, then the degree of ∠C is () | D | ['135°', '122.5°', '115.5°', '112.5°'] | multi_choice |
geo345 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/345.png | As shown in the figure, in △ABC, AB=AC, ∠B=70°, then the degree of ∠A is () | D | ['70°', '55°', '50°', '40°'] | multi_choice |
geo346 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/346.png | As shown in the figure, line a is parallel to line b, AC is perpendicular to AB, AC intersects line b at point C, and ∠2 = 42°. What is the degree of ∠1? | C | ['38°', '42°', '48°', '58°'] | multi_choice |
geo347 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/347.png | As shown in the figure: There is a cylinder with a height of 8 cm and a base diameter of 4 cm (π=3). There is an ant at point A on the lower base of the cylinder. It wants to reach the food at point B on the upper base directly opposite A. What is the approximate shortest distance the ant needs to crawl? | A | ['10cm', '12cm', '19cm', '20cm'] | multi_choice |
geo348 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/348.png | As shown in the figure, A, B, C, and D are four points in sequence on the straight line L. M and N are the midpoints of AB and CD, respectively, and MN = 6 cm, BC = 1 cm. What is the length of AD? | B | ['10cm', '11cm', '12cm', '13cm'] | multi_choice |
geo349 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/349.png | As shown in the figure, line AB is perpendicular to line CD at point O, and line EF passes through point O. If ∠1 = 26°, then what is the measure of ∠2? | B | ['26°', '64°', '54°', '以上答案都不对'] | multi_choice |
geo350 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/350.png | As shown in the figure, given that AB ∥ CD and ∠2 = 135°, what is the degree of ∠1? | B | ['35°', '45°', '55°', '65°'] | multi_choice |
geo351 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/351.png | As shown in the figure, AB is the diameter of circle O, and points C and D are on circle O. If ∠BAC = 50°, then what is ∠ADC? | A | ['40°', '50°', '80°', '100°'] | multi_choice |
geo352 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/352.png | As shown in the figure, AB = AC, AD ∥ BC, ∠BAC = 100°, then the degree of ∠CAD is () | C | ['30°', '35°', '40°', '50°'] | multi_choice |
geo353 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/353.png | As shown in the figure, place the right-angle vertex of an isosceles right triangle on one side of a ruler. If ∠1 = 40°, then ∠2 = () | C | ['40°', '45°', '50°', '60°'] | multi_choice |
geo354 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/354.png | As shown in the figure, points A and C to be measured are separated by a pond. Master Li randomly selects a point B outside of AC, connects BA and BC, and takes the midpoints E and F of BA and BC, respectively. The distance between points E and F is measured to be 23 meters. What is the distance between points A and C? | A | ['46', '23', '50', '25'] | multi_choice |
geo355 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/355.png | As shown in the figure, the two sides of ∠AOB, OA and OB, are plane mirrors, and ∠AOB = 40°. There is a point P on the ray OB. A beam of light is emitted from point P, reflected at point Q on OA, and the reflected light QR is exactly parallel to OB. What is the measure of ∠QPB? | B | ['60°', '80°', '100°', '120°'] | multi_choice |
geo356 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/356.png | As shown in the figure, if △ABC is rotated 25° clockwise around point C to obtain △A'B'C, and A'B' intersects AC at D. Given that ∠A'DC=90°, what is the measure of ∠A? | C | ['45°', '55°', '65°', '25°'] | multi_choice |
geo357 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/357.png | As shown in the figure, a shepherd is herding horses at point A. The shepherd's home is at point B. The distances from A and B to the riverbank, AC and BD, are 500 meters and 700 meters respectively. The distance between points C and D is 1600 meters. Before it gets dark, the shepherd leads the horse from point A to th... | C | ['2600米', '2300米', '2000米', '1200米'] | multi_choice |
geo358 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/358.png | As shown in the figure, OA is perpendicular to OB. If ∠1 = 42°, then what is the measure of ∠2? | D | ['52°', '58°', '42°', '48°'] | multi_choice |
geo359 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/359.png | As shown in the figure, in △ABC, BD and CE are the medians of △ABC, intersecting at point O. Points F and G are the midpoints of OB and OC, respectively. Connect AO. If AO = 3 cm and BC = 4 cm, what is the perimeter of quadrilateral DEFG? | A | ['7cm', '9cm', '12cm', '14cm'] | multi_choice |
geo360 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/360.png | As shown in the figure, AB is parallel to CD, and ∠A = 50°. What is the degree of ∠1? | C | ['40°', '50°', '130°', '150°'] | multi_choice |
geo361 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/361.png | As shown in the figure, in the parallelogram ABCD, if ∠A + ∠C = 100°, then the measure of ∠B is () | A | ['130°', '80°', '100°', '50°'] | multi_choice |
geo362 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/362.png | As shown in the figure, place two vertices of a right triangle with a 45° angle on the opposite sides of a ruler. If ∠1 = 22°, then the measure of ∠2 is () | B | ['30°', '23°', '22°', '15°'] | multi_choice |
geo363 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/363.png | As shown in the figure: If m is parallel to n, and ∠1 = 105°, then ∠2 = () | D | ['55°', '60°', '65°', '75°'] | multi_choice |
geo364 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/364.png | As shown in the figure, in the parallelogram ABCD, the bisector of ∠BAD intersects BC at point E, and the bisector of ∠ABC intersects AD at point F. Connect EF. If BF = 12 and AB = 10, what is the length of AE? | A | ['16', '15', '14', '13'] | multi_choice |
geo365 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/365.png | As shown in the figure, a//b, ∠1=65°, ∠2=140°, then ∠3=() | B | ['100°', '105°', '110°', '115°'] | multi_choice |
geo366 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/366.png | As shown in the figure, point O is inside triangle ABC, and the distances to the three sides are equal. If ∠A = 60°, then what is the measure of ∠BOC? | B | ['135°', '120°', '90°', '60°'] | multi_choice |
geo367 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/367.png | As shown in the figure, line AB and line CD intersect at point O. OE is perpendicular to CD, and ∠AOE = 52°. What is the measure of ∠BOD? | A | ['38°', '42°', '48°', '52°'] | multi_choice |
geo368 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/368.png | As shown in the figure, point A is one endpoint of the diameter of a protractor, point B is on the semicircle, point P is on segment AB, and point Q is on AB, with PB = PQ. If point P corresponds to 140° (40°), what is the measure of ∠PQB? | B | ['65°', '70°', '75°', '80°'] | multi_choice |
geo369 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/369.png | As shown in the figure, points D and E are the midpoints of sides AB and AC of the inscribed equilateral triangle ABC in circle O, respectively. If the radius of circle O is 2, then the length of DE is equal to () | A | ['√{3}', '√{2}', '1', '\\frac{√{3}}{2}'] | multi_choice |
geo370 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/370.png | As shown in the figure, circle O intersects all three sides of triangle ABC, and the segments DE, FG, and HK intercepted on the three sides are equal. Given that ∠A = 50°, what is the measure of ∠BOC? | C | ['130°', '120°', '115°', '105°'] | multi_choice |
geo371 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/371.png | As shown in the figure, in the right triangle ABC, ∠C=90°, ∠B=25°. With C as the center and the length of CA as the radius, a circle intersects AB at point D. What is the degree measure of arc AD? | B | ['25°', '50°', '45°', '30°'] | multi_choice |
geo372 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/372.png | As shown in the figure, the vertices A, B, and D of the parallelogram ABCD are on the circle O, and the vertex C is on the diameter BE of the circle O. Given that ∠ADC = 53°, connect AE. What is the measure of ∠AEB? | A | ['37°', '46°', '27°', '63°'] | multi_choice |
geo373 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/373.png | As shown in the figure, the radius of circle O is 5, the chord AB = 5√3, and C is a point on the circle. What is the measure of ∠ACB? | C | ['30°', '45°', '60°', '90°'] | multi_choice |
geo374 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/374.png | As shown in the figure, AB is the diameter of circle O, ∠BAC=42°, point D is the midpoint of chord AC, then what is the degree of ∠DOC? | C | ['58°', '50°', '48°', '42°'] | multi_choice |
geo375 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/375.png | As shown in the figure, points A, B, and C are on circle O. If ∠AOB = 62°, then ∠ACB equals () | C | ['29°', '30°', '31°', '32°'] | multi_choice |
geo376 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/376.png | As shown in the figure, AD is the diameter of the semicircle, point C is the midpoint of arc BD, and ∠ADC=55°. What is the measure of ∠BAD? | D | ['50°', '55°', '65°', '70°'] | multi_choice |
geo377 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/377.png | As shown in the figure, AB is the diameter of circle O, point C is on circle O, CD bisects ∠ACB and intersects circle O at point D. If ∠ABC = 30°, then what is the measure of ∠CAD? | B | ['l00°', '105°', '110°', '120'] | multi_choice |
geo378 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/378.png | As shown in the figure, AB is the diameter of circle O, and C and D are points on circle O. If ∠ADC = 20°, what is the measure of ∠CAB? | C | ['40°', '80°', '70°', '50°'] | multi_choice |
geo379 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/379.png | As shown in the figure, AB is the diameter of circle O, and chord CD is perpendicular to AB at point E. Connect OC and BD. If ∠AOC = 110°, what is the measure of ∠ABD? | C | ['35°', '46°', '55°', '70°'] | multi_choice |
geo380 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/380.png | As shown in the figure, ∠A is the inscribed angle of circle O, and ∠A = 40°. What is the degree of ∠OBC? | B | ['40°', '50°', '60°', '80°'] | multi_choice |
geo381 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/381.png | As shown in the figure, AB is the diameter of circle O, and points C and D are on circle O. If ∠ACD = 15°, what is the measure of ∠BAD? | A | ['75°', '72°', '70°', '65°'] | multi_choice |
geo382 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/382.png | As shown in the figure, points A, B, C, and D are on circle O. OB is parallel to CD, and ∠A = 25°. What is the measure of ∠BOD? | C | ['100°', '120°', '130°', '150°'] | multi_choice |
geo383 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/383.png | As shown in the figure: Given that AB is the diameter of circle O, point C is on circle O, and point D is on radius OA (not coinciding with points O and A). If ∠COA = 60°, ∠CDO = 70°, what is the measure of ∠ACD? | D | ['60°', '50°', '30°', '10°'] | multi_choice |
geo384 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/384.png | As shown in the figure, given that points A, B, and C are on circle O, and ∠C = 35°, what is the measure of ∠AOB? | B | ['75°', '70°', '60°', '35°'] | multi_choice |
geo385 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/385.png | As shown in the figure, points A, B, and C are on circle O. If ∠AOB = 130°, then the measure of ∠C is () | C | ['150°', '130°', '115°', '120°'] | multi_choice |
geo386 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/386.png | As shown in the figure, AB is the diameter of semicircle O, point C is a point on semicircle O, D is the midpoint of segment AC, and ∠DAC = 40°. What is the measure of ∠CAB? | A | ['10°', '15°', '20°', '25°'] | multi_choice |
geo387 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/387.png | As shown in the figure, BC is the diameter of circle O, and points A and D are on circle O. If ∠D = 36°, then what is the degree measure of ∠BCA? | C | ['36°', '45°', '54°', '72°'] | multi_choice |
geo388 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/388.png | As shown in the figure, points A, B, and C are on circle O, and D is the midpoint of segment AB. If ∠ACD = 20°, what is the measure of ∠AOB? | C | ['60°', '70°', '80°', '90°'] | multi_choice |
geo389 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/389.png | As shown in the figure, points A, B, and C are all on circle O. If ∠BAC = 36°, then the measure of ∠BOC is () | B | ['75°', '72°', '64°', '54°'] | multi_choice |
geo390 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/390.png | As shown in the figure, AB is the diameter of circle O, and C and D are two points on circle O. If ∠AOC = 130°, then what is the measure of ∠D? | C | ['65°', '35°', '25°', '15°'] | multi_choice |
geo391 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/391.png | As shown in the figure ⊙O, OA ⊥ BC, ∠AOC = 50°, then the measure of ∠ADB is () | B | ['15°', '25°', '30°', '50°'] | multi_choice |
geo392 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/392.png | As shown in the figure, in the acute triangle ABC, AD and CE are the altitudes on sides BC and AB, respectively, with the feet of the perpendiculars being D and E, respectively. AD and CE intersect at point O. If ∠B = 60°, then what is the measure of ∠AOE? | A | ['60°', '50°', '70°', '80°'] | multi_choice |
geo393 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/393.png | The cross-section of an arc-shaped vegetable greenhouse in a certain vegetable base is shown in the figure. Given that AB=16m and the radius OA=10m, what is the height of the middle column CD? | B | ['3m', '4m', '5m', '6m'] | multi_choice |
geo394 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/394.png | As shown in the figure, the cross-section of a cylindrical drainage pipe is given. It is known that the distance from the center O to the water surface OC is 3 dm, the width of the water surface AB is 8 dm. What is the diameter of the cross-section of the drainage pipe? | B | ['16dm', '10dm', '8dm', '6dm'] | multi_choice |
geo395 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/395.png | As shown in the figure, AB is the diameter of circle O, and chord CD is perpendicular to AB. If ∠CAB = 25°, then what is ∠BOD? | C | ['70°', '65°', '50°', '45°'] | multi_choice |
geo396 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/396.png | As shown in the figure, place a ruler with scales on both sides on a semicircular piece of paper, so that one side passes through the center O, and the other side intersects the semicircle at points D and E. Measure the radius OC = 5cm, and the chord DE = 8cm. What is the width of the ruler? | C | ['1cm', '2cm', '3cm', '4cm'] | multi_choice |
geo397 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/397.png | As shown in the figure, in △ABC, ∠C=30°, AD is the altitude on side BC, and ∠DAB=20°. What is the measure of ∠BAC? | A | ['80°', '70°', '60°', '50°'] | multi_choice |
geo398 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/398.png | As shown in the figure, a triangular plate overlaps with a circular disc. The right-angle sides AB and AC are both equal to 2, and AB coincides with the diameter of the circular disc. What is the area of the shaded part? | D | ['1+\\frac{π}{4}', '2-\\frac{π}{4}', '2', '1'] | multi_choice |
geo399 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/399.png | As shown in the figure, circles A, B, and C do not intersect with each other, and the radius of each is 2 cm. What is the total area of the three sectors (i.e., the three shaded parts) in the figure? | B | ['4πcm^{2}', '2πcm^{2}', 'πcm^{2}', '\\frac{π}{2}cm^{2}'] | multi_choice |
geo400 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/400.png | As shown in the figure, the radius of the base of the cone is 3, and the slant height is 6. What is the lateral surface area? | D | ['8π', '6π', '12π', '18π'] | multi_choice |
geo401 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/401.png | A large sunshade umbrella, when opened, can be approximately considered as a conical shape, as shown in the figure. The slant height is 2.5 meters, and the radius of the base is 2 meters. What is the area of the fabric needed to make this sunshade umbrella (excluding seams)? | B | ['\\frac{25}{4}π', '5π', '4π', '3π'] | multi_choice |
geo402 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/402.png | As shown in the figure, four circles with a radius of 1 are externally tangent to each other. What is the area of the shaded region? | A | ['π', '2π', '3π', '4π'] | multi_choice |
geo403 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/403.png | As shown in the figure, AB is the diameter of circle O, ∠BAC=30°, CD is perpendicular to AB at point E, BE=2, then the length of AC is () | A | ['4√{3}', '6', '4', '6√{3}'] | multi_choice |
geo404 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/404.png | As shown in the figure, there is a sector with a central angle of 120° and a radius of 6 cm. If OA and OB are overlapped to form the lateral surface of a cone, what is the height of the cone? | A | ['4√{2}', '2√{3}', '2√{2}', '4√{3}'] | multi_choice |
geo405 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/405.png | As shown in the figure, a sector of a circle with a central angle of 120° and a radius of 6 cm is rolled into a cone-shaped paper hat without a bottom. What is the height of this paper hat? | C | ['√{2}cm', '3√{2}cm', '4√{2}cm', '4cm'] | multi_choice |
geo406 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/406.png | A sector of paper with a central angle of 90° and a radius of 16 cm is rolled into a bottomless conical paper hat (seam not considered), as shown in the figure. What is the radius of the base of this paper hat? | B | ['8cm', '4cm', '16cm', '2cm'] | multi_choice |
geo407 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/407.png | As shown in the figure, there is a sector of paper with a central angle of 90° and a radius of 12 cm. It is used to form the lateral surface of a cone (ignoring the seam). What is the radius of the base of the cone? | B | ['2cm', '3cm', '4cm', 'πcm'] | multi_choice |
geo408 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/408.png | As shown in the figure, the lateral surface of a cone is a sector with a radius of 3 and a central angle of 90°. What is the radius of the base circle of the cone? | C | ['\\frac{3}{4}π', '\\frac{3}{2}π', '\\frac{3}{4}', '\\frac{3}{2}'] | multi_choice |
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