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
values |
|---|---|---|---|---|---|
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 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 |
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 O. If the distance between points M and N is 100 nautical miles, what is the measure of ∠NOF? | 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 the river to drink water and then returns home. What is the minimum distance the shepherd needs to walk? | 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 |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.