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geo819 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/819.png | As shown in the figure, when building a pumping station, a pipeline is laid along a slope with an inclination angle of 30°. If the length of the water pipe AB is measured to be 80 meters, what is the height BC of point B from the horizontal plane? | 40米 | NULL | free_form |
geo830 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/830.png | As shown in the figure, given that points A, B, and C are on circle O, and ∠A = 50°, what is the degree measure of ∠BOC? | 100° | NULL | free_form |
geo833 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/833.png | As shown in the figure, △ABC is inscribed in circle O, AD is the diameter of circle O, and ∠ABC = 35°. What is the measure of ∠CAD? | 55° | NULL | free_form |
geo844 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/844.png | As shown in the figure, quadrilateral ABCD is a rhombus. The lengths of the two diagonals are AC = 26 cm and BD = 10 cm. What is the area of rhombus ABCD? | 130cm² | NULL | free_form |
geo845 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/845.png | As shown in the figure, the diagonals AC and BD of the rhombus ABCD intersect at point O. If AO = 3 cm and BO = 4 cm, what is the area of the rhombus ABCD in cm²? | 24 | NULL | free_form |
geo846 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/846.png | As shown in the figure, in the rhombus ABCD, points E and F are the midpoints of AB and AC, respectively. The perimeter of the rhombus ABCD is 32. What is the length of EF? | 4 | NULL | free_form |
geo847 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/847.png | As shown in the figure, P is a point on the diagonal BD of the rhombus ABCD. PE is perpendicular to AB at E, and PE = 4 cm. What is the distance from point P to BC? | 4cm | NULL | free_form |
geo855 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/855.png | As shown in the figure, the diagonals AC and BD of parallelogram ABCD intersect at O. E is the midpoint of side BC. Connect OE. Given that AB = 6, what is the length of OE? | 3 | NULL | free_form |
geo857 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/857.png | As shown in the figure, in parallelogram ABCD, diagonals AC and BD intersect at point O, and point E is the midpoint of BC. If OE = 4 cm, then the length of AB is () | 8cm | NULL | free_form |
geo860 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/860.png | In parallelogram ABCD, ∠BAD=110°, ∠ABD=30°, then the degree of ∠CBD is () | 40° | NULL | free_form |
geo868 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/868.png | As shown in the figure, in the parallelogram ABCD, CE is perpendicular to AB, and ∠D = 53°. What is the measure of ∠BCE? | 37° | NULL | free_form |
geo871 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/871.png | As shown in the figure, given that in parallelogram ABCD, ∠A = 154°, what is ∠B equal to? | 26° | NULL | free_form |
geo879 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/879.png | As shown in the figure, in a parallelogram with a perimeter of 18 cm, AC and BD intersect at point O. OE is perpendicular to BD and intersects AD at E. What is the perimeter of triangle △ABE? | 9cm | NULL | free_form |
geo885 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/885.png | As shown in the figure, given that points A, B, and C are on circle O, and ∠ACB = 30°, then what is ∠AOB equal to? | 60° | NULL | free_form |
geo888 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/888.png | As shown in the figure, AB is the diameter of circle O, and points C and D are on circle O. If ∠C = 40°, then what is the degree of ∠ABD? | 50° | NULL | free_form |
geo890 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/890.png | As shown in the figure, AB is the diameter of circle O, and CD is a chord of circle O. Connect AD, DB, and BC. If ∠ABD = 55°, what is the measure of ∠BCD? | 35° | NULL | free_form |
geo891 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/891.png | OA and OB are two radii of circle O, and ∠C = 40°, point C is on circle O, then the degree of ∠AOB is () | 80° | NULL | free_form |
geo892 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/892.png | As shown in the figure, A, B, and C are three points on the circle with center O. If ∠ABC = 25°, what is the measure of ∠AOC? | 50° | NULL | free_form |
geo893 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/893.png | As shown in the figure, points A, B, and P are on the circle. If ∠APB = 40°, then ∠AOB equals () | 80° | NULL | free_form |
geo895 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/895.png | As shown in the figure, ⊙O is the circumcircle of △ABC. Given that ∠OAB = 40°, what is the measure of ∠ACB? | 50° | NULL | free_form |
geo899 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/899.png | As shown in the figure, points A, B, and C are on circle O, and ∠AOB=90°. What is the degree of ∠C? | 45° | NULL | free_form |
geo901 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/901.png | As shown in the figure, given that points A, B, and C are on circle O, and ∠BAC = 25°, what is the degree measure of ∠OCB? | 65° | NULL | free_form |
geo903 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/903.png | As shown in the figure, in circle O, ∠BOC = 80°, then the measure of ∠A is () | 40° | NULL | free_form |
geo904 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/904.png | As shown in the figure, points A, B, and C are on circle O. If ∠AOB = 80°, then ∠ACB equals () | 40° | NULL | free_form |
geo905 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/905.png | As shown in the figure, AB is the diameter of circle O, and points D and C are on circle O. AD is parallel to OC, and ∠DAB = 60°. Connect AC, then what is ∠DAC equal to? | 30° | NULL | free_form |
geo907 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/907.png | As shown in the figure, △ABC is inscribed in circle O, and ∠BOC = 80°. What is the measure of ∠BAC? | 40° | NULL | free_form |
geo909 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/909.png | As shown in the figure, A and D are two points on the circle O, and BC is the diameter. If ∠D = 35°, what is the degree of ∠ACB? | 55° | NULL | free_form |
geo912 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/912.png | As shown in the figure, AB is the diameter of circle O, and C and D are two points on circle O. Connect AC, BC, CD, and OD. If ∠DOB = 140°, then ∠ACD = () | 20° | NULL | free_form |
geo913 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/913.png | As shown in the figure, in circle O, if ∠BAC is known to be 48°, then the degree of ∠BOC is () | 96° | NULL | free_form |
geo916 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/916.png | As shown in the figure, AB is the diameter of circle O. If ∠ADC = 55°, then what is the measure of ∠BAC? | 35° | NULL | free_form |
geo918 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/918.png | As shown in the figure, AT is the tangent to circle O, and AB is the chord of circle O. Given that ∠B = 55°, what is the measure of ∠BAT? | 35° | NULL | free_form |
geo926 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/926.png | As shown in the figure, AB is the diameter of circle O, and CD is a chord of circle O. If ∠ABD = 63°, then what is ∠BCD? | 27° | NULL | free_form |
geo932 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/932.png | As shown in the figure, given that AB∥CE and ∠A=110°, what is the measure of ∠ADE? | 110° | NULL | free_form |
geo941 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/941.png | As shown in the figure, line AB is parallel to line CD, ∠C = 36°, ∠E is a right angle, then ∠A equals () | 54° | NULL | free_form |
geo948 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/948.png | As shown in the figure, given that point C is on line segment AB, points M and N are the midpoints of AC and BC respectively, and AB = 8 cm, what is the length of MN? | 4cm | NULL | free_form |
geo949 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/949.png | As shown in the figure, AB ∥ CD, EF ⊥ AB at E, EF intersects CD at F. Given that ∠1 = 60°, find ∠2. | 30° | NULL | free_form |
geo961 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/961.png | As shown in the figure, AB ∥ CD, AE intersects CD at C, ∠A = 35°, ∠DEC = 90°, then the degree of ∠D is () | 55° | NULL | free_form |
geo964 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/964.png | Point P is a point on the side AB of square ABCD (not coinciding with A or B). Connect PD and rotate the segment PD 90° clockwise around point P to get segment PE. Connect BE. What is the measure of ∠CBE? | 45° | NULL | free_form |
geo967 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/967.png | As shown in the figure, the diagonals AC and BD of parallelogram ABCD intersect at point O. Points E and F are the midpoints of segments AO and BO, respectively. If AC + BD = 24 cm and the perimeter of △OAB is 18 cm, then EF is () | 3cm | NULL | free_form |
geo968 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/968.png | As shown in the figure, a∥b, ∠3=135°, then the degree of ∠1 is () | 45° | NULL | free_form |
geo979 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/979.png | As shown in the figure, quadrilateral ABCD is inscribed in circle O. If one of its exterior angles ∠DCE is 70°, then ∠BOD = () | 140° | NULL | free_form |
geo981 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/981.png | As shown in the figure, in rectangle ABCD, AB=4, AD=3, what is the value of cosα? | \frac{4}{5} | NULL | free_form |
geo988 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/988.png | As shown in the figure, D is a point on side AB of △ABC, rac{AD}{AB}= rac{2}{3}, DE∥BC intersects AC at E, DE=6, then BC=() | 9 | NULL | free_form |
geo990 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/990.png | As shown in the figure, in △ABC, points D and E are on sides AB and AC respectively, and DE ∥ BC. Given that DE = 6 and rac{AD}{DB} = rac{3}{4}, what is the length of BC? | 14 | NULL | free_form |
geo991 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/991.png | As shown in the figure, given that the slope of the hill AB is 1:2 and BC=1, what is the length of the slope AB? | √{5} | NULL | free_form |
geo992 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/992.png | As shown in the figure, DE ∥ BC, and \( \frac{AD}{BD} = \frac{1}{3} \), then \( \frac{DE}{BC} \) equals () | \frac{1}{4} | NULL | free_form |
geo997 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/997.png | In △ABC, right triangles △ABD and △ACE are constructed with AB and AC as the hypotenuses, respectively. ∠ADB = ∠AEC = 90°, ∠ABD = ∠ACE = 30°. Connect ED. If DE = 5, then what is the length of BC? | 10 | NULL | free_form |
geo999 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/999.png | As shown in the figure, in △ABC, DE∥BC, AD:AB=1:3, if the area of △ADE is 3, then the area of △ABC is () | 27 | NULL | free_form |
geo1001 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/1001.png | As shown in the figure, points A, B, and C are on the circle with center O. If ∠AOB = 80°, then what is the measure of ∠ACB? | 40° | NULL | free_form |
geo1003 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/1003.png | As shown in the figure, given that AB is the diameter of the circumcircle of triangle ABC, and ∠A = 32°, what is the measure of ∠B? | 58° | NULL | free_form |
geo1006 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/1006.png | As shown in the figure, given that ⊙O is the circumcircle of △ABD, AB is the diameter of ⊙O, CD is a chord of ⊙O, and ∠ABD=50°, then ∠BCD equals () | 40° | NULL | free_form |
geo1010 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/1010.png | As shown in the figure, points A, B, and C are on the circle with center O, and ∠OAB = 55°. What is the measure of ∠ACB in degrees? | 35 | NULL | free_form |
geo1012 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/1012.png | As shown in the figure, points A, B, and C are all on circle O. If ∠AOB = 68°, then the measure of ∠ACB is () | 34° | NULL | free_form |
geo1013 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/1013.png | As shown in the figure, points A, B, and C are on circle O, and ∠AOB = 40°. What is the degree measure of ∠ACB? | 20° | NULL | free_form |
geo1015 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/1015.png | As shown in the figure, in circle O, chord AB is parallel to chord CD. If ∠ABC = 50°, then ∠BOD is equal to () | 100° | NULL | free_form |
geo1016 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/1016.png | As shown in the figure, A, B, and C are three points on circle O. If ∠AOC = 50°, what is the measure of ∠ABC? | 25° | NULL | free_form |
geo1017 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/1017.png | As shown in the figure, points A, B, and C are on the circle ⊙O. If ∠ACB = 35°, then the measure of ∠AOB is () | 70° | NULL | free_form |
geo1022 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/1022.png | As shown in the figure, ⊙O is the circumcircle of △ABC, and ∠OCB=35°. What is the degree of ∠A? | 55° | NULL | free_form |
geo1023 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/1023.png | As shown in the figure, AB is the diameter of the semicircle O, ∠BAC=60°, D is any point on the semicircle, then the degree of ∠D is () | 30° | NULL | free_form |
geo1029 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/1029.png | As shown in the figure, △ABC is inscribed in circle O, CD is the diameter of circle O, and ∠BCD=50°. What is the measure of ∠A? | 40° | NULL | free_form |
geo1030 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/1030.png | As shown in the figure, points A, B, and C are on circle O. If ∠BOC = 76°, what is the measure of ∠BAC? | 38° | NULL | free_form |
geo1033 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/1033.png | As shown in the figure, in circle O, AB is the diameter, ∠BAD=30°, what is the degree of ∠C? | 60° | NULL | free_form |
geo1035 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/1035.png | As shown in the figure, AB is the diameter of circle O, and C and D are two points on circle O. If ∠BAC = 50°, what is the measure of ∠ADC? | 40° | NULL | free_form |
geo1036 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/1036.png | As shown in the figure, A, B, and C are points on the circle with center O. If ∠AOB = 70°, what is the measure of ∠ACB? | 35° | NULL | free_form |
geo1040 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/1040.png | As shown in the figure, AB is a chord of circle O. From any point on the circle, draw a chord CD perpendicular to AB. Draw the bisector of ∠OCD, which intersects circle O at point P. If AP = 5, what is the value of BP? | 5 | NULL | free_form |
geo33 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/33.png | find \tan S. | 0.75 | NULL | free_form |
geo81 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/81.png | Trapezoid P Q R S has an area of 250 square inches. Find the height of P Q R S. | A | ['10', '15', '20', '25'] | multi_choice |
geo141 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/141.png | Use a Pythagorean Triple to find x. | C | ['22', '25', '28', '31'] | multi_choice |
geo177 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/177.png | In \odot H, P Q = 3 x - 4 and R S = 14. Find x. | B | ['4', '6', '8', '16'] | multi_choice |
geo228 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/228.png | Find m \widehat B C. | C | ['21', '63', '123', '155'] | multi_choice |
geo279 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/279.png | Circle W has a radius of 4 units, \odot Z has a radius of 7 units, and X Y = 2. Find I X. | B | ['2', '6', '12', '18'] | multi_choice |
geo295 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/295.png | Find y. | D | ['6', '17', '\\frac { 289 } { 6 }', '\\frac { 325 } { 6 }'] | multi_choice |
geo301 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/301.png | As shown in the figure, given that AB ∥ CD and ∠1 = 56°, what is the degree of ∠2? | B | ['34°', '56°', '65°', '124°'] | multi_choice |
geo308 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/308.png | As shown in the figure, the perimeter of triangle △ABC is 21, and AB=AC, BC=5. The perpendicular bisector of AB, DE, intersects AB at point D and intersects AC at point E. What is the perimeter of △BEC? | A | ['13', '14', '15', '16'] | 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 |
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 |
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 |
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 |
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 |
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 |
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 |
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 |
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 |
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 |
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 |
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 |
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 |
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 |
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 |
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 |
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 |
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 |
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 |
geo512 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/512.png | As shown in the figure, in the inscribed pentagon ABCDE of circle O, ∠CAD = 42°, then the sum of ∠B and ∠E is () | B | ['220°', '222°', '225°', '228°'] | multi_choice |
geo544 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/544.png | As shown in the figure, △ABC is inscribed in circle O, C is the midpoint of arc AB, and D is a point on circle O. Given that ∠ACB = 100°, what is the measure of ∠ADC? | A | ['40°', '39°', '38°', '36°'] | multi_choice |
geo591 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/591.png | As shown in the figure, the three sides of △ABC are tangent to circle O at points D, E, and F respectively. If ∠A = 50°, then what is ∠DEF? | A | ['65°', '50°', '130°', '80°'] | multi_choice |
geo604 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/604.png | As shown in the figure, two concentric circles have the same center O. The chord AB of the larger circle is a tangent to the smaller circle. If the radius of the larger circle is 10 cm and the radius of the smaller circle is 6 cm, what is the length of the chord AB? | D | ['8cm', '10cm', '12cm', '16cm'] | multi_choice |
geo606 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/606.png | AB is the diameter of circle O, and chord CD is tangent to circle O, with AB ∥ CD. If chord CD = 16 cm, what is the area of the shaded region? | B | ['144πcm²', '64πcm²', '79πcm²', '81πcm²'] | multi_choice |
geo610 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/610.png | As shown in the figure, in quadrilateral ABCD, E and F are on AD and BC respectively. AB ∥ EF ∥ DC, and DE = 3, DA = 5, CF = 4. What is the length of FB? | B | ['\\frac{3}{2}', '\\frac{8}{3}', '5', '6'] | multi_choice |
geo612 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/612.png | As shown in the figure, AD ∥ BE ∥ CF, lines l_{1}, l_{2} intersect these three parallel lines at points A, B, C and points D, E, F respectively. If AB = 2, BC = 4, DF = 9, then what is the length of EF? | B | ['3', '6', '7', '8'] | multi_choice |
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