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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geo809 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/809.png | As shown in the figure, a square ABCD with a diagonal length of 2√2 is moved along the direction of the diagonal AC, moving point A to the midpoint A' of the line segment AC to obtain a new square A'B'C'D'. The overlapping part of the new square and the original square is a smaller square (shaded part). What is the area of the smaller square? | 1 | NULL | free_form |
geo810 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/810.png | As shown in the figure, DE intersects the sides AB and AC of triangle ABC at points D and E, respectively, and DE is parallel to BC. If AD:BD = 3:1 and DE = 6, then what is the length of BC? | 8 | NULL | free_form |
geo811 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/811.png | As shown in the figure, in △ABC, AB=AC, D and E are the midpoints of AB and AC respectively, and points G and F are on BC. DEFG is a square, and DE=2cm. What is the length of AC? | 2√{5}cm | NULL | free_form |
geo812 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/812.png | As shown in the figure, in parallelogram ABCD, point E is on DC. If EC:AB=2:3 and EF=4, what is the length of BF? | 6 | NULL | free_form |
geo813 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/813.png | As shown in the figure, in the parallelogram ABCD, CE is the bisector of ∠DCB and intersects AB at E. DB intersects CE at O. Given that AB=6 and BC=4, then rac{OB}{DB} equals () | \frac{2}{5} | NULL | free_form |
geo814 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/814.png | As shown in the figure, in the parallelogram ABCD, E is a point on side BC, and AE intersects BD at point F. If \(\frac{BE}{BC} = \frac{2}{3}\), then the value of \(\frac{BF}{FD}\) is () | \frac{2}{3} | NULL | free_form |
geo815 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/815.png | The cross-section of the river embankment is as shown in the figure. The height of the embankment is 10 meters, the length of the water-facing slope BC is 26 meters, and the tangent value of the slope angle ∠ACB is () | \frac{5}{12} | NULL | free_form |
geo816 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/816.png | As shown in the figure, the cross-section of the reservoir dam is trapezoidal. The top width of the dam is 6 meters, the height of the dam is 8 meters, the slope angle of slope AB is 45°, and the slope of slope CD is i=1:3. What is the width of the dam base BC? | 38m | NULL | free_form |
geo817 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/817.png | As shown in the figure, the heavy snow in 2008 broke Grandpa Zhang's electric wires. In order to ensure that Grandpa Zhang, who lives on the hillside, can use electricity during the 2008 Spring Festival, the relevant departments plan to pull wires (2 household electric wires) from the foot of the mountain along the slope. The measured angle between the slope and the horizontal plane is 30°, and the vertical height is 38m. How long is the electric wire needed? | 152m | NULL | free_form |
geo818 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/818.png | As shown in the figure, in order to green the barren mountain, a certain place plans to lay water pipes from the well house at the foot of the mountain along the slope, and build a pumping station on the slope to spray the green area on the slope. It is now measured that the angle between the slope and the horizontal plane is 30°. To make the height of the water outlet 35m, how long should the water pipe be prepared? | 70m | NULL | free_form |
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 |
geo820 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/820.png | As shown in the figure, the detector of the hot air balloon indicates that the angle of elevation from the hot air balloon A to the top of a building B is 30°, and the angle of depression to the bottom of the building C is 60°. The horizontal distance from the hot air balloon A to the building is 120 meters. What is the height of the building? | 160√{3}m | NULL | free_form |
geo821 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/821.png | As shown in the figure, the plane detects its target C directly below it at point B in the air. At this time, the flight altitude AC is 1200 meters. The tangent value of the depression angle α from the plane to the ground command post A is rac{3}{4}. What is the distance AB between the plane and the command post? | 2000 | NULL | free_form |
geo822 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/822.png | As shown in the figure, at the top of a cliff 100 meters above sea level at point A, an observer measures the depression angle to a small boat B on the sea surface to be 30°. What is the horizontal distance between the boat and the observer? | 100√{3} | NULL | free_form |
geo823 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/823.png | As shown in the figure, in order to measure the height of the building, the angle of depression from the top of the building A to a point B on the ground is 30°. It is known that the horizontal distance BC from this point on the ground to the building is 30 meters. What is the height AC of the building? | 10√{3}m | NULL | free_form |
geo824 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/824.png | As shown in the figure, in order to measure the height of the flagpole BC on the school playground, the angle of elevation of the top of the flagpole is measured to be 30° at point A, which is 24 meters away from the flagpole. What is the height of the flagpole? | 8√{3}米 | NULL | free_form |
geo825 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/825.png | As shown in the figure: Xiaojun wants to measure the distance from the small island B in the river to the riverbank L. At point A, the angle ∠BAD is measured to be 30°, and at point C, the angle ∠BCD is measured to be 60°. It is also measured that AC = 10 meters. What is the distance from the small island B to the riverbank L? | 5√{3} | NULL | free_form |
geo826 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/826.png | As shown in the figure, there is a simple folding dining table. It is measured that OA=OB=40cm, OC=OD=60cm. Now, if the height of the table from the ground is required to be 50cm, what should be the angle ∠COD between the two table legs? | 120° | NULL | free_form |
geo827 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/827.png | As shown in the figure, in the parallelogram ABCD, through A, draw AM intersecting BD at point P, intersecting CD at point N, and intersecting the extension line of BC at point M. If AB=7, AD=10, and CM=4, what is the length of DN? | 5 | NULL | free_form |
geo828 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/828.png | As shown in the figure, AB is tangent to circle O at point C, and OA = OB. If the diameter of circle O is 8 cm and AB = 10 cm, what is the length of OA? | √{41} | NULL | free_form |
geo829 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/829.png | As shown in the figure, there are two scale points C and D on the protractor, which are 40° and 60° respectively. O is the origin, and OB is the 0-degree line. What is the degree of ∠DAC? | 10° | 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 |
geo831 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/831.png | As shown in the figure, in circle O, ∠AOC = 160°, then ∠ABC is equal to () | 80° | NULL | free_form |
geo832 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/832.png | As shown in the figure, AC is the diameter of circle O, and AB and CD are two chords of circle O, with AB ∥ CD. If ∠BAC = 32°, then what is the measure of ∠AOD? | 64° | 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 |
geo834 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/834.png | In a plane rectangular coordinate system, there is a semicircular piece (with a central angle ∠AED=52°) placed as shown in the figure. If point A can slide up and down along the positive half of the y-axis, and point B slides along the positive half of the x-axis, when ∠OAB=n°, the distance between point D on the semicircular piece and the origin O is maximized. What is the value of n? | 26° | NULL | free_form |
geo835 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/835.png | As shown in the figure, quadrilateral ABCD is a square with a side length of 8. Point E is on side CD, and CE = 6. Draw EF parallel to BC, intersecting AC and AB at points G and F respectively. M and N are the midpoints of AG and BE respectively. What is the length of MN? | 5 | NULL | free_form |
geo836 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/836.png | As shown in the figure, the lines l1, l2, l3, and l4 are parallel to each other, and the distance between any two adjacent parallel lines is equal to 1. If the four vertices of the square ABCD are on these four lines respectively, what is its area? | 5 | NULL | free_form |
geo837 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/837.png | Fold rectangle ABCD along AE to obtain the shape shown in the figure. Given that ∠CED' = 60°, what is the measure of ∠AED? | 60° | NULL | free_form |
geo838 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/838.png | As shown in the figure, there is a rectangular field ABCD with length AB=102 and width AD=51. The width of the middle road from entrances A and B is 1, and the width of the road at the junction of the two small roads is 2. The rest of the area is planted with grass. What is the area of the grass? | 5000 | NULL | free_form |
geo839 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/839.png | As shown in the figure, in rectangle ABCD, AB=5, AD=12, M is any point on AD other than A and D, and ME is perpendicular to AC at E, MF is perpendicular to BD at F, then what is the value of ME+MF? | \frac{60}{13} | NULL | free_form |
geo840 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/840.png | As shown in the figure, E is the midpoint of side BC of rectangle ABCD, and ∠BAE=30°, AE=2. What is the length of AC? | √{7} | NULL | free_form |
geo841 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/841.png | As shown in the figure, P is a point on the diagonal AC of the rhombus ABCD. PE is perpendicular to AB at point E, and PF is perpendicular to AD at point F. If PF = 3 cm, then the length of the distance from point P to AB, PE, is () | 3cm | NULL | free_form |
geo842 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/842.png | As shown in the figure, the perimeter of rhombus ABCD is 8, and E is the midpoint of AB. What is OE? | 1 | NULL | free_form |
geo843 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/843.png | As shown in the figure, in rhombus ABCD, ∠DAC=25°, then ∠B=() | 130° | 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 |
geo848 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/848.png | As shown in the figure, in the rhombus ABCD, it is known that AB=10 and AC=16. What is the area of the rhombus ABCD? | 96 | NULL | free_form |
geo849 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/849.png | As shown in the figure, in the rhombus ABCD, ∠C=110°, the perpendicular bisector of BC intersects BD at point E, F is the foot of the perpendicular, connect AE, then the degree of ∠EAD is () | 75° | NULL | free_form |
geo850 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/850.png | As shown in the figure, fold the parallelogram ABCD along the diagonal AC so that point B falls on B'. If ∠1 = ∠2 = 44°, then what is ∠B? | 114° | NULL | free_form |
geo851 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/851.png | As shown in the figure, in parallelogram ABCD, use a ruler and compass to draw the bisector of ∠BAD, which intersects BC at point E. If BF=6 and AB=5, then the length of AE is () | 8 | NULL | free_form |
geo852 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/852.png | As shown in the figure, given that the area of parallelogram ABCD is 48, E is the midpoint of AB. Connect DE and OE. What is the area of △ODE? | 6 | NULL | free_form |
geo853 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/853.png | As shown in the figure, in parallelogram ABCD, EF passes through the intersection point O of the diagonals. If AD = 6, AB = 5, and OE = 2, what is the perimeter of quadrilateral ABFE? | 15 | NULL | free_form |
geo854 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/854.png | As shown in the figure, in parallelogram ABCD, AB=6, AD=9, ∠BAD=120°, and the bisector of ∠BAD intersects BC at point E and intersects the extension of DC at point F. What is the perimeter of △CEF? | 9 | 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 |
geo856 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/856.png | As shown in the figure, the diagonals AC and BD of parallelogram ABCD intersect at point O. Point E is the midpoint of AD. The perimeter of triangle BCD is 18. What is the perimeter of triangle DEO? | 9 | 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 |
geo858 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/858.png | As shown in the figure, the perimeter of parallelogram ABCD is 36. The diagonals AC and BD intersect at point O. Point E is the midpoint of CD, and BD = 12. What is the perimeter of triangle DOE? | 15 | NULL | free_form |
geo859 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/859.png | As shown in the figure, in the parallelogram ABCD, AE bisects ∠DAB, and ∠B = 110°. What is ∠DEA equal to? | 35° | 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 |
geo861 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/861.png | As shown in the figure, in the parallelogram ABCD, a perpendicular line is drawn from the intersection point O of the diagonals AC and BD to AC, intersecting AD at point E. Connect CE. If AB = 4 and BC = 6, what is the perimeter of triangle CDE? | 10 | NULL | free_form |
geo862 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/862.png | As shown in the figure, in the parallelogram ABCD, ∠ABD=50°, AF is perpendicular to BC at F, AF intersects BD at E, point O is the midpoint of DE, connect OA. If DE=2AB, then the size of ∠ADB is () | 25° | NULL | free_form |
geo863 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/863.png | As shown in the figure, in parallelogram ABCD, AB=4, AD=7, the bisector of ∠BCD intersects AD at point E and intersects the extension of BA at point F. What is the length of AF? | 3 | NULL | free_form |
geo864 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/864.png | As shown in the figure, in parallelogram ABCD, ∠B = 70°, point E is the midpoint of BC, point F is on AB, and BF = BE. Draw FG perpendicular to CD at point G through point F. What is the measure of ∠EGC? | 55° | NULL | free_form |
geo865 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/865.png | As shown in the figure, in the parallelogram ABCD, AE and DF are the angle bisectors of ∠BAD and ∠ADC respectively, intersecting at point G and intersecting side BC at points E and F. Given that AD=8 and EF=2, find the length of side AB of the parallelogram. | 5 | NULL | free_form |
geo866 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/866.png | As shown in the figure, in a parallelogram, two pairs of lines parallel to the sides divide this parallelogram into nine smaller parallelograms. If the area of the original parallelogram is 100 cm², and the area of the middle small parallelogram (shaded part) is 20 cm², then the area of quadrilateral ABDC is () | 60cm² | NULL | free_form |
geo867 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/867.png | As shown in the figure, in parallelogram ABCD, extend CD to point E, extend AD to point F, and connect EF. If ∠B = 110°, then ∠E + ∠F = () | 70° | 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 |
geo869 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/869.png | As shown in the figure, in parallelogram ABCD, point M is the midpoint of CD, and DC = 2AD. What is the degree of the angle between AM and BM? | 90° | NULL | free_form |
geo870 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/870.png | As shown in the figure, in parallelogram ABCD, EF passes through the intersection point O of the diagonals. AB=4, AD=3, OF=1.5. What is the perimeter of quadrilateral BCEF? | 10 | 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 |
geo872 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/872.png | As shown in the figure, in the parallelogram ABCD, AB=3, BC=4, BE bisects ∠ABC and intersects AD at E. What are the lengths of AE and ED respectively? | 1 | NULL | free_form |
geo873 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/873.png | Given: As shown in the figure, in the parallelogram ABCD, AB=4, AD=7, the bisector of ∠ABC intersects AD at point E. Find the length of ED. | 3 | NULL | free_form |
geo874 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/874.png | As shown in the figure, in parallelogram ABCD, it is known that diagonals AC and BD intersect at point O. The perimeter of triangle AOB is 15 cm, and AB = 6 cm. What is the sum of AC and BD? | 18cm | NULL | free_form |
geo875 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/875.png | In the parallelogram ABCD shown in the figure, AB=3, AC=4, BC=5, then the area of parallelogram ABCD is () | 12 | NULL | free_form |
geo876 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/876.png | As shown in the figure, in the parallelogram ABCD, ∠C = 108°, BE bisects ∠ABC, then ∠AEB equals () | 36° | NULL | free_form |
geo877 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/877.png | As shown in the figure, chord AB of circle O1 is the tangent line of circle O2, and AB is parallel to O1O2. If AB = 12 cm, then the area of the shaded part is () | 36πcm² | NULL | free_form |
geo878 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/878.png | As shown in the figure, the perimeter of the parallelogram is 28 cm, and the perimeter of △ABC is 22 cm. What is the length of AC? | 8厘米 | 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 |
geo880 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/880.png | As shown in the figure, in the isosceles triangle △ABC, AB=AC=5, BC=6, E is any point on the side BC. Draw EM∥AB through E, intersecting AC at M, and EN∥AC, intersecting AB at N. Then the perimeter of the parallelogram AMEN is () | 10 | NULL | free_form |
geo881 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/881.png | As shown in the figure, in the parallelogram ABCD, AE is perpendicular to BC at E, AF is perpendicular to the extension line of DC at point F, and ∠EAF = 40°. What is the measure of ∠B? | 40° | NULL | free_form |
geo882 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/882.png | As shown in the figure, AB is the diameter of circle O, and ∠ACD = 15°. What is the measure of ∠ABD? | 15° | NULL | free_form |
geo883 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/883.png | As shown in the figure, given that ∠BAC=35°, arc CD=80°, what is the measure of ∠BOD? | 150° | NULL | free_form |
geo884 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/884.png | As shown in the figure, the diameter BD of circle O is 6, and ∠A is 60°. What is the length of BC? | 3√{3} | 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 |
geo886 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/886.png | As shown in the figure, AB is the diameter of the semicircle O, and ∠DBA = 20°. What is the measure of ∠C? | 110° | NULL | free_form |
geo887 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/887.png | As shown in the figure, ∠C is the inscribed angle of circle O, and ∠C = 38°. Then, ∠OAB = () degrees. | 52 | 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 |
geo889 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/889.png | As shown in the figure, it is known that the line l intersects the circle O at points E and F. AB is the diameter of the circle O, and AD is perpendicular to l at point D. If ∠DAE = 22°, then what is the measure of ∠BAF? | 22° | 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 |
geo894 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/894.png | As shown in the figure, AB is the diameter of circle O, and ∠BAD=70°. What is the measure of ∠ACD? | 20° | 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 |
geo896 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/896.png | As shown in the figure, ⊙O is the circumcircle of △ABC, and ∠BOC = 110°. What is the measure of ∠A? | 55° | NULL | free_form |
geo897 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/897.png | As shown in the figure, in circle O, chords AB and CD intersect at P. If ∠A = 30°, ∠APD = 60°, then ∠B equals () | 30° | NULL | free_form |
geo898 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/898.png | As shown in the figure, AB is the diameter of circle O, and chord CD is perpendicular to AB at point E. G is an arbitrary point on AC. Connect AD and GD. If arc BC is 50°, then ∠AGD = () | 65° | 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 |
geo900 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/900.png | As shown in the figure, in circle O, AD and BC are chords of circle O, OA is perpendicular to BC, ∠AOB = 50°, CE is perpendicular to AD, then the measure of ∠DCE is () | 65° | 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 |
geo902 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/902.png | As shown in the figure, C is a point on the semicircle O with AB as its diameter. Connect AC and BC, and construct squares ACDE and BCFG outward with AC and BC as sides, respectively. The midpoints of DE, FG, AC, and BC are M, N, P, and Q, respectively. If MP + NQ = 12 and AC + BC = 16, what is the length of AB? | 12 | 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 |
geo906 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/906.png | As shown in the figure, in circle O, A, B, C, and D are all on the circle. ∠BAC=25°, ∠CED=30°, then what is the degree of ∠BOD? | 110° | 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 |
geo908 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/908.png | As shown in the figure, in circle O, OD is perpendicular to BC, and ∠CAD = 40°. What is the measure of ∠BOD? | 80° | NULL | free_form |
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