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 |
|---|---|---|---|---|---|
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 |
geo910 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/910.png | As shown in the figure, points A, B, and C are on the circle O, and ∠BOC = 60°. What is ∠BAC equal to? | 30° | NULL | free_form |
geo911 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/911.png | As shown in the figure, in circle O, ∠ABC=30°, then the degree of ∠AOC is () | 60° | 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 |
geo914 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/914.png | As shown in the figure, in circle O, ∠BAC = 25°, then the degree of ∠BOC is () | 50° | NULL | free_form |
geo915 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/915.png | As shown in the figure, AB is the diameter of the semicircle O, and D is a point on AC. If ∠BAC = 35°, then what is the measure of ∠ADC? | 125° | 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 |
geo917 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/917.png | As shown in the figure, given that A, B, and C are on circle O, and ∠A = ∠B = 19°, what is the measure of ∠AOB? | 76° | 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 |
geo919 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/919.png | As shown in the figure, the radius of circle B is 4 cm, ∠MBN = 60°, points A and C are moving points on rays BM and BN respectively, and line AC is perpendicular to BN. When AC is translated to be tangent to circle B, what is the length of AB? | 8cm | NULL | free_form |
geo920 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/920.png | As shown in the figure, AE is tangent to circle D at point E. Given AC = CD = DB = 10, find the length of segment AE. | 10√{3} | NULL | free_form |
geo921 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/921.png | As shown in the figure, △ABC is inscribed in circle O, and DE is the tangent to circle O at point A. If ∠ABC = 50°, then ∠CAE equals () | 50° | NULL | free_form |
geo922 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/922.png | In the figure, EB is the diameter of the semicircle O, point A is on the extension of EB, AD is tangent to the semicircle O at point D, BC is perpendicular to AD at point C, AB=2, and the radius of the semicircle O is 2. What is the length of BC? | 1 | NULL | free_form |
geo923 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/923.png | As shown in the figure, points A, B, C, and D are on circle O. If ∠B = 100°, then what is the degree of ∠ADE? | 100° | NULL | free_form |
geo924 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/924.png | As shown in the figure, a student with a height of 1.6m wants to measure the height of the school flagpole. When he stands at point C, the top of his shadow coincides with the top of the flagpole's shadow. It is measured that AC=2m and BC=8m. What is the height of the flagpole? | 8m | NULL | free_form |
geo925 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/925.png | As shown in the figure, in △ABC, AB=6, AC=7, BC=5, the perpendicular bisector of side AB intersects AC at point D. What is the perimeter of △BDC? | 12 | 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 |
geo927 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/927.png | Fold a rectangular piece of paper as shown in the figure. If ∠1 = 40°, what is the degree of ∠2? | 70° | NULL | free_form |
geo928 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/928.png | As shown in the figure, quadrilateral ABCD is an inscribed quadrilateral in circle O. If ∠BOD = 90°, then the measure of ∠BCD is () | 135° | NULL | free_form |
geo929 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/929.png | As shown in the figure, in △ABC, ∠B=32°. △ABC is folded along the line m, and point B falls at the position of point D. What is the degree of ∠1 - ∠2? | 64° | NULL | free_form |
geo930 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/930.png | As shown in the figure, ∠1 = 68°, line a is translated to obtain line b, then the degree of ∠2 - ∠3 is () | 112° | NULL | free_form |
geo931 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/931.png | As shown in the figure, in △ABC, it is known that AB=AC, DE is the perpendicular bisector of AC, and ∠A=50°. What is the degree of ∠DCB? | 15° | 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 |
geo933 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/933.png | As shown in the figure, in the isosceles triangle ABC, AB=AC, ∠A=40°, the perpendicular bisector of segment AB intersects AB at point D and intersects AC at point E. Connect BE, then ∠CBE equals () | 30° | NULL | free_form |
geo934 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/934.png | Mathematics is everywhere in our lives, even on a small billiard table there are mathematical problems. As shown in the figure, ∠1 = ∠2. If ∠3 = 25°, in order for the white ball to rebound and directly hit the black ball into the bottom pocket, what must be the value of ∠1 when hitting the white ball? | 65° | NULL | free_form |
geo935 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/935.png | As shown in the figure, point A is on the line BG, AD is parallel to BC, AE bisects ∠GAD. If ∠CBA = 80°, then ∠GAE = () | 50° | NULL | free_form |
geo936 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/936.png | As shown in the figure, a road returns to its original direction after two turns. If the angle at the first turn, ∠B, is 140°, what is the degree of ∠C? | 140° | NULL | free_form |
geo937 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/937.png | As shown in the figure, points B, D, and C are on the circle O, and ∠BDC=130°. What is ∠BOC? | 100° | NULL | free_form |
geo938 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/938.png | As shown in the figure, in △ABC, ∠A=90°, AB=AC, BD bisects ∠ABC and intersects AC at point D, DE is perpendicular to BC at point E. If the perimeter of △CDE is 8cm, then the length of the hypotenuse BC is () | 8cm | NULL | free_form |
geo939 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/939.png | As shown in the figure, in △ABC, ∠A=∠B=50°, AK=BN, AM=BK, what is the degree of ∠MKN? | 50° | NULL | free_form |
geo940 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/940.png | As shown in the figure, in the heptagon ABCDEFG, the extensions of AB and ED intersect at point O. If the sum of the adjacent supplementary angles corresponding to ∠1, ∠2, ∠3, and ∠4 is 215°, what is the measure of ∠BOD? | 35° | 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 |
geo942 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/942.png | As shown in the figure, a right-angled triangle paper ABC (∠ACB=90°) is folded along the line segment CD, making point B fall on B'. If ∠ACB' = 70°, then the degree of ∠ACD is (). | 10° | NULL | free_form |
geo943 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/943.png | As shown in the figure, AB is a chord of circle O, OC is perpendicular to AB, intersecting circle O at point C. Connect OA, OB, and BC. If ∠ABC = 15°, then what is the measure of ∠AOB? | 60° | NULL | free_form |
geo944 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/944.png | As shown in the figure, it is known that DC∥FP, ∠1=∠2, ∠FED=32°, ∠AGF=76°, FH bisects ∠EFG. What is the degree of ∠PFH? | 22° | NULL | free_form |
geo945 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/945.png | As shown in the figure, place the vertex of the 45° angle of a triangular ruler on one side of a straight ruler. When ∠1 = 63°, what is ∠2? | 72° | NULL | free_form |
geo946 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/946.png | As shown in the figure, in order to estimate the width of the river, a target point A is selected on the opposite bank of the river. Points B, C, D, and E are taken on the near bank such that points A, B, and D are on a straight line, and AD is perpendicular to DE. Points A, C, and E are also on a straight line and DE is parallel to BC. If BC = 24m, BD = 12m, and DE = 40m, what is the approximate width of the river AB? | 18m | NULL | free_form |
geo947 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/947.png | As shown in the figure, a∥b. Place the right-angle vertex of the triangle ruler on line a. If ∠1=40°, then ∠2=() | 50° | 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 |
geo950 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/950.png | As shown in the figure, ⊙I is the inscribed circle of △ABC, and D, E, F are the three points of tangency. If ∠DEF = 52°, then the measure of ∠A is () | 76° | NULL | free_form |
geo951 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/951.png | As shown in the figure, AB is a chord of circle O, and PA is a tangent to circle O. If ∠PAB = 40°, then ∠AOB = () | 80° | NULL | free_form |
geo952 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/952.png | As shown in the figure, the radius of circle B is 4 cm, ∠MBN = 60°, points A and C are moving points on rays BM and BN respectively, and line AC is perpendicular to BN. When AC is translated to be tangent to circle B, what is the length of AB? | 8cm | NULL | free_form |
geo953 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/953.png | As shown in the figure, triangle ABC is translated along the direction of AB to reach the position of triangle BDE. If ∠CAB = 50° and ∠ABC = 100°, then the measure of ∠1 is () | 30° | NULL | free_form |
geo954 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/954.png | As shown in the figure, the line BC intersects MN at point O, AO is perpendicular to BC, and OE bisects ∠BON. If ∠EON = 20°, what is the measure of ∠AOM? | 50° | NULL | free_form |
geo955 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/955.png | As shown in the figure, AB∥CD∥EF, AC∥DF. If ∠BAC=120°, then the degree of ∠DFE is () | 120° | NULL | free_form |
geo956 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/956.png | As shown in the figure, AB ∥ CD, ∠ABE = 120°, ∠ECD = 25°, then ∠E = () | 85° | NULL | free_form |
geo957 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/957.png | As shown in the figure, in △ABC, AB=AC, ∠A=40°, a semicircle with AB as the diameter intersects BC and AC at points D and E respectively. What is the degree measure of arc BD? | 40° | NULL | free_form |
geo958 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/958.png | As shown in the figure, at 9 AM, a boat departs from point A and sails due north at a speed of 20 li/hour. It reaches point B at 11 AM. From points A and B, the angles to the lighthouse C are measured as ∠NAC=36° and ∠NBC=72°, respectively. What is the distance from point B to the lighthouse C? | 40里 | NULL | free_form |
geo959 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/959.png | As shown in the figure, place the right-angled vertex C of the right-angled triangle ABC with a 30° angle on one side of the ruler. Given that ∠A = 30° and ∠1 = 40°, what is the degree of ∠2? | 70° | NULL | free_form |
geo960 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/960.png | As shown in the figure, lines a and b intersect at point O. If ∠1 = 30°, then ∠2 equals () | 150° | 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 |
geo962 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/962.png | As shown in the figure, given that the line segment AB = 20 cm, C is the midpoint of AB, D is a point on CB, E is the midpoint of DB, and EB = 3 cm, then CD equals () | 4cm | NULL | free_form |
geo963 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/963.png | As shown in the figure, in △ABC, point D is on side BC, BD=AD=AC, E is the midpoint of CD. If ∠CAE=16°, then the measure of ∠B is () | 37° | 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 |
geo965 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/965.png | As shown in the figure, given that the area of square B is 144 and the area of square C is 169, what is the area of square A? | 25 | NULL | free_form |
geo966 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/966.png | As shown in the figure, A, B, and C are three points on circle O. If ∠ACB = 20°, then what is the measure of ∠AOB? | 40° | 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 |
geo969 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/969.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 = 15°, then what is the degree of ∠2? | 30° | NULL | free_form |
geo970 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/970.png | As shown in the figure, given that lines AB, CD, and EF intersect at point O, ∠1 = 95°, ∠2 = 53°, what is the measure of ∠BOE? | 32° | NULL | free_form |
geo971 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/971.png | As shown in the figure, if AB ∥ CD, then ∠α = 130°, ∠β = 80°, then ∠γ = () | 30° | NULL | free_form |
geo972 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/972.png | As shown in the figure, triangle △ABC is folded along DE and EF, with vertices A and B both falling on point O, and EA and EB overlapping with line segment EO. If ∠CDO + ∠CFO = 106°, what is the measure of ∠C? | 37° | NULL | free_form |
geo973 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/973.png | As shown in the figure, lines a and b intersect, ∠1=130°, then ∠2+∠3=() | 100° | NULL | free_form |
geo974 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/974.png | As shown in the figure, the rectangular paper is folded along the dashed line in Figure ① for the first time to get Figure ②. The crease forms an angle ∠1=65° with one side of the rectangle. Then, the paper is folded along the dashed line in Figure ② for the second time to get Figure ③. What is the degree of ∠2? | 25° | NULL | free_form |
geo975 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/975.png | As shown in the figure, lines AB and CD intersect at point O, and OE bisects ∠AOD. If ∠COE = 140°, then ∠BOC = () | 80° | NULL | free_form |
geo976 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/976.png | As shown in the figure, points A, B, and C are on circle O, AB is parallel to CO, and ∠B = 22°. What is ∠A? | 44° | NULL | free_form |
geo977 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/977.png | Given that AB ∥ CD and ∠ACD = 55°, find ∠BAC. | 55° | NULL | free_form |
geo978 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/978.png | As shown in the figure, parallelogram ABCD is rotated counterclockwise by 40° around point D to obtain parallelogram A'B'C'D (point A' is the corresponding point of point A, point B' is the corresponding point of point B, and point C' is the corresponding point of point C), and point A' falls exactly on side AB. What is the measure of ∠B? | 110° | 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 |
geo980 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/980.png | As shown in the figure, the front view and the left view of a spatial geometric body are both equilateral triangles with a side length of 1, and the top view is a circle. What is the lateral surface area of this geometric body? | \frac{π}{2} | 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 |
geo982 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/982.png | As shown in the figure, given that AB is the diameter of circle O, CD is a chord and CD ⊥ AB, BC = 6, AC = 8, what is the value of sin∠ABD? | \frac{4}{5} | NULL | free_form |
geo983 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/983.png | In triangle △ABC, ∠C=90°, BC=5, AB=13, what is the value of sinA? | \frac{5}{13} | NULL | free_form |
geo984 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/984.png | As shown in the figure, extend the hypotenuse AB of the right triangle △ABC to point D, making BD = AB. Connect CD. If cot∠BCD = 3, then the value of tan∠A is () | \frac{3}{2} | NULL | free_form |
geo985 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/985.png | As shown in the figure, in △ABC, DE∥BC, and AE:EC=1:3. If the area of △ABC is 16, what is the area of △ADE? | 1 | NULL | free_form |
geo986 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/986.png | As shown in the figure, in △ABC, DE∥BC, rac{DE}{BC}= rac{1}{3}, AD=2. What is the value of BD? | 4 | NULL | free_form |
geo987 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/987.png | As shown in the figure, in △ABC, point D is a point on side AB, ∠ACD=∠B, AD=1, AC=2. If the area of △ADC is 0.8, then the area of △BCD is () | 2.4 | 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 |
geo989 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/989.png | As shown in the figure, in △ABC, point D is a point on side AB. If ∠ACD = ∠B, AD = 1, AC = 2, and the area of △ADC is 3, then what is the area of △BCD? | 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 |
geo993 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/993.png | As shown in the figure, in the square ABCD, G is the midpoint of side CD. Connect AG and extend it to intersect the extension line of side BC at point E. The diagonal BD intersects AG at point F. Given that FG = 2, what is the length of segment AE? | 12 | NULL | free_form |
geo994 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/994.png | As shown in the figure, in parallelogram ABCD, AD = 18, points E and F are on BD and CD respectively, EF is parallel to BC, and \(\frac{DE}{EB} = \frac{1}{2}\). Then EF equals () | 6 | NULL | free_form |
geo995 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/995.png | As shown in the figure, in the right triangle ABC, ∠C=90°, ∠A=30°, CD is perpendicular to AB at D. What is the ratio of the perimeters of △CBD and △ABC? | \frac{1}{2} | NULL | free_form |
geo996 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/996.png | As shown in the figure, in △ABC, points D and E are on sides AB and AC respectively, and DE ∥ BC. If the ratio of the perimeters of △ADE to △ABC is 2:3, and AD = 4, then the length of DB is () | 2 | 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 |
geo998 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/998.png | As shown in the figure, in △ABC, D is a point on BC, ∠BAD=∠C, AB=6, BD=4, then the length of CD is () | 5 | 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 |
geo1000 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/1000.png | As shown in the figure, the diameter AB of circle O is perpendicular to chord CD, and ∠BAC = 40°. What is the measure of ∠BOD? | 80° | 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 |
geo1002 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/1002.png | As shown in the figure, △ABC is an inscribed triangle in circle O, AC is the diameter of circle O, ∠C=60°, the angle bisector of ∠ABC, BD, intersects circle O at point D. What is the measure of ∠BAD? | 75° | 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 |
geo1004 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/1004.png | As shown in the figure, points A, B, and C are on circle O. Given that ∠B = 52° and ∠C = 18°, what is the measure of ∠A? | 34° | NULL | free_form |
geo1005 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/1005.png | As shown in the figure, points A, B, and C are on the circle with center O, and ∠ABD = 70°, AB = BD. What is the measure of ∠O? | 110° | 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 |
geo1007 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/1007.png | As shown in the figure, the diameter of the protractor coincides with the hypotenuse AB of the right triangle ABC. The endpoint N of the 0-degree line of the protractor coincides with point A. Ray CP starts from CA and rotates clockwise at a speed of 2 degrees per second. CP intersects the semicircular arc of the protractor at point E. What is the corresponding degree on the protractor at point E at the 30th second? | 120° | NULL | free_form |
geo1008 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/1008.png | As shown in the figure, in circle A with a radius of 5, chords BC and ED correspond to central angles ∠BAC and ∠EAD, respectively. Given that DE = 6 and ∠BAC + ∠EAD = 180°, what is the distance from the center to chord BC? | 3 | NULL | free_form |
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