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 |
|---|---|---|---|---|---|
geo709 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/709.png | As shown in the figure, point C is on line segment AB, and point D is the midpoint of AC. If CD = 3 and AB = 10, what is the length of BC? | D | ['3', '3.5', '4.5', '4'] | multi_choice |
geo710 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/710.png | As shown in the figure, it is known that point C divides the line segment AB into two parts in the ratio 1:2 from left to right. Point D is the midpoint of AB. If DC = 2, then the length of the line segment AB is () | C | ['10', '11', '12', '13'] | multi_choice |
geo711 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/711.png | As shown in the figure, line segment AB = 10 cm, point C is a point on line segment AB, BC = 3 cm, points D and E are the midpoints of AC and AB respectively. What is the length of line segment DE? | C | ['\\frac{1}{2}', '1', '\\frac{3}{2}', '2'] | multi_choice |
geo712 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/712.png | As shown in the figure, points A, B, C, D, and E are all on circle O, ⌒{AC}=⌒{AE}, ∠D=128°, then the degree of ∠B is () | D | ['128°', '126°', '118°', '116°'] | multi_choice |
geo713 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/713.png | As shown in the figure, in circle O, arc AB is equal to arc AC, and angle A is 40°. What is the measure of angle B? | D | ['60°', '40°', '50°', '70°'] | multi_choice |
geo714 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/714.png | To measure the inclination of the slope pad shown in the figure, Xiao Ming drew a side view diagram of the slope pad. The measured data are: ∠ABC=90°, AB=15cm, AC=35cm. What is the sine value of the inclination angle α? | A | ['\\frac{3}{7}', '\\frac{7}{3}', '\\frac{2}{3}√{10}', '\\frac{3}{20}√{10}'] | multi_choice |
geo715 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/715.png | As shown in the figure, the slope ratio of the upstream slope AB of the cross-section of the river dam is 3:4, and BC = 6m. What is the length of the slope AB? | C | ['6m', '8m', '10m', '12m'] | multi_choice |
geo716 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/716.png | The cross-section of the river embankment is as shown in the figure. The slope of slope AB is 1:√3, and BC is 5 meters. What is the length of AC in meters? | A | ['5√{3}', '5', '15', '10√{3}'] | multi_choice |
geo717 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/717.png | As shown in the figure, in △ABC, DE∥BC, AD=8, DB=4, AE=6, then the length of EC is () | C | ['1', '2', '3', '4'] | multi_choice |
geo718 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/718.png | Definition: In an isosceles triangle, the ratio of the base to the leg is called the opposite of the vertex angle. The opposite of vertex angle A is denoted as sadA, i.e., sadA = base:leg. As shown in the figure, in △ABC, AB = AC, and ∠A = 2∠B. Then sinB • sadA = () | B | ['\\frac{1}{2}', '1', '√{2}', '2'] | multi_choice |
geo719 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/719.png | As shown in the figure, △ABC is an inscribed triangle of circle O, ∠ABC=30°, AC=6. What is the diameter of circle O? | B | ['6', '12', '6√{2}', '6√{3}'] | multi_choice |
geo720 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/720.png | As shown in the figure, in △ABC, AB=4, AC=2, BC=5, point I is the incenter of △ABC. Translate ∠BAC so that its vertex coincides with point I. What is the perimeter of the shaded area in the figure? | B | ['4', '5', '6', '7'] | multi_choice |
geo721 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/721.png | As shown in the figure, in the right triangle ABC, AC=6, AB=10, what is the value of sinA? | A | ['\\frac{4}{5}', '\\frac{3}{5}', '\\frac{3}{4}', '\\frac{4}{3}'] | multi_choice |
geo722 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/722.png | As shown in the figure, in the right triangle ABC, ∠C=90°, AB=10, BC=8, then sinA=() | B | ['\\frac{3}{5}', '\\frac{4}{5}', '\\frac{3}{4}', '\\frac{4}{3}'] | multi_choice |
geo723 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/723.png | As shown in the figure, quadrilateral ABCD and A'B'C'D' are similar figures with point O as the center of similarity. If OA':OA = 3:5 and the area of quadrilateral A'B'C'D' is 9 cm^2, then the area of quadrilateral ABCD is () | B | ['15cm^2^', '25cm^2^', '18cm^2^', '27cm^2^'] | multi_choice |
geo724 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/724.png | As shown in the figure, ⊙O is the inscribed circle of △ABC, AC=10, AB=8, BC=9. Points D and E are on BC and AC respectively, and DE is the tangent to ⊙O. What is the perimeter of △CDE? | C | ['9', '7', '11', '8'] | multi_choice |
geo725 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/725.png | As shown in the figure, E and F are the midpoints of sides AD and BC of rectangle ABCD, respectively. If rectangle ABCD is similar to rectangle EABF, and AB = 1, then what is the area of rectangle ABCD? | D | ['4', '2', '√{3}', '√{2}'] | multi_choice |
geo726 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/726.png | As shown in the figure, △ABO is similar to △CDO. If AB=12, CD=4, and AO=9, what is the length of CO? | 3 | NULL | free_form |
geo727 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/727.png | As shown in the figure, the shape of a paraglider is a quadrilateral ABCD that is symmetrical about the vertical axis. Given that ∠B = 40° and ∠CAD = 60°, find ∠BCD. | 160° | NULL | free_form |
geo728 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/728.png | As shown in the figure, points A and B are on the same side of line l, AB = 4 cm, point C is the symmetric point of point B with respect to line l, AC intersects line l at point D, AC = 5 cm. What is the perimeter of triangle △ABD? | 9cm | NULL | free_form |
geo729 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/729.png | In △ABC, AB=AC=6, from the construction traces, the length of DE is () | 3 | NULL | free_form |
geo730 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/730.png | As shown in the figure, in △ABC, the bisectors of ∠ABC and ∠ACB intersect at point O. Through point O, draw MN parallel to BC, intersecting AB and AC at points M and N, respectively. If AB=12, AC=18, and BC=24, what is the perimeter of △AMN? | 30 | NULL | free_form |
geo731 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/731.png | The positional relationship of several roads in a certain city is shown in the figure. It is known that AB∥CD, the angle between AE and AB is 48°, and the lengths of CF and EF are equal. What is the degree of angle ∠C? | 24° | NULL | free_form |
geo732 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/732.png | As shown in the figure, in △ABC, AB=AC, CD∥AB, point E is on the extension of BC. If ∠A=30°, then the measure of ∠DCE is () | 75° | NULL | free_form |
geo733 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/733.png | As shown in the figure, AE ∥ BD, C is a point on BD, and AB = BC, ∠ACD = 110°, then the degree of ∠EAB is () | 40° | NULL | free_form |
geo734 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/734.png | As shown in the figure, in △ABC, AB=AC, AE bisects ∠BAC, DE is the perpendicular bisector of AB, connect CE, ∠B=70°. Then the degree of ∠BCE is () | 50° | NULL | free_form |
geo735 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/735.png | As shown in the figure, given that the area of parallelogram ABCD is 24 cm^2, point P is a moving point on side CD. What is the area of the shaded part in the figure? | 12cm^2^ | NULL | free_form |
geo736 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/736.png | As shown in the figure, in parallelogram ▱ABCD, AD=10, AB=8, P is any point on BC, and E, F, G, H are the midpoints of AB, AP, DP, and DC respectively. What is the length of EF+GH? | 5 | NULL | free_form |
geo737 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/737.png | As shown in the figure, in parallelogram ABCD, diagonals AC and BD intersect at point O. E is the midpoint of side BC. If OE = 2 and AD = 5, what is the perimeter of parallelogram ABCD? | 18 | NULL | free_form |
geo738 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/738.png | As shown in the figure, in the parallelogram ABCD, point E is the midpoint of side AB, and point F is the midpoint of diagonal AC. If EF = 6, then what is the length of AD? | 12 | NULL | free_form |
geo739 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/739.png | As shown in the figure, in the parallelogram ABCD, the diagonals AC and BD intersect at point O. The line segments MN, PQ, and EF pass through point O. Given that BC = 10 and the height from BC is 6, find the area of the shaded region. | 30 | NULL | free_form |
geo740 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/740.png | As shown in the figure, two square strips with widths of 1 and 2 are placed crosswise, and the overlapping part is quadrilateral ABCD. If AB + BC = 6, what is the area of quadrilateral ABCD? | 4 | NULL | free_form |
geo741 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/741.png | As shown in the figure, point O is the midpoint of AC. A parallelogram ABCD with a perimeter of 8 cm is translated along the diagonal AC by the length of AO to obtain parallelogram OB'C'D'. What is the perimeter of quadrilateral OECF? | 4cm | NULL | free_form |
geo742 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/742.png | As shown in the figure, in parallelogram ABCD, AB = 2AD, ∠A = 60°, E and F are the midpoints of AB and CD respectively, and EF = 1cm. What is the length of diagonal BD? | √{3}cm | NULL | free_form |
geo743 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/743.png | As shown in the figure, point D is inside triangle ABC, CD bisects ∠ACB, BD is perpendicular to CD, ∠A = ∠ABD, if AC = 6 and BC = 4, then the length of BD is () | 1 | NULL | free_form |
geo744 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/744.png | As shown in the figure, in △ABC, AC + BC = 24, AO and BO are angle bisectors, and MN ∥ BA, intersecting AC at N and BC at M, respectively. What is the perimeter of △CMN? | 24 | NULL | free_form |
geo745 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/745.png | As shown in the figure, in △ABC, D and E are the midpoints of BC and AC respectively, and DE is parallel to AB. BF bisects ∠ABC and intersects DE at point F. If BC = 8, what is the length of DF? | 4 | NULL | free_form |
geo746 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/746.png | As shown in the figure, in △ABC, AB=6, AC=9, BD and CD bisect ∠ABC and ∠ACB respectively. A line passing through point D is drawn parallel to BC, intersecting AB and AC at points E and F respectively. What is the perimeter of △AEF? | 15 | NULL | free_form |
geo747 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/747.png | As shown in the figure, in △ABC, BE bisects ∠ABC, CE bisects ∠ACB, and BE and CE intersect at point E. Through point E, draw MN parallel to BC, intersecting AB at point M and AC at point N. If MN = 8, then the length of BM + CN is () | 8 | NULL | free_form |
geo748 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/748.png | As shown in the figure, in △ABC, the angle bisector of ∠ABC intersects AC at point D, and AD = 6. Draw DE through point D parallel to BC, intersecting AB at point E. If the perimeter of △AED is 16, then the length of side AB is () | 10 | NULL | free_form |
geo749 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/749.png | As shown in the figure, in △ABC, CE bisects ∠ACB, point D is on the extension line of BC, CF bisects ∠ACD, and EF is parallel to BC and intersects AC at M. If CM = 5, then what is the value of CE^2 + CF^2? | 100 | NULL | free_form |
geo750 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/750.png | Given that the line DE intersects the two sides AC and AB of the scalene triangle △ABC at points D and E respectively, and ∠CAB=60°, then in the figure, what is ∠CDE + ∠BED? | 240° | NULL | free_form |
geo751 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/751.png | As shown in the figure, two equilateral triangles with areas of 9 and 16 respectively overlap, resulting in two shaded areas with areas a and b (a < b). What is the value of b - a? | 7 | NULL | free_form |
geo752 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/752.png | As shown in the figure, there are two identical triangular plates with a 30° angle, denoted as △ABC and △A1B1C1. Now, the two triangular plates are overlapped, and the midpoint of the longer right-angle side is M. Rotate the upper triangular plate ABC around the midpoint M, and the right-angle vertex C just falls on the hypotenuse A1B1 of the triangular plate △A1B1C1. When ∠A=30° and B1C=2, what is the length of AB at this time? | 8 | NULL | free_form |
geo753 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/753.png | As shown in the figure, given ∠ABC=120°, BD bisects ∠ABC, ∠DAC=60°, if AB=2 and BC=3, then the length of BD is () | 5 | NULL | free_form |
geo754 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/754.png | As shown in the figure, in right triangle ABC, ∠C=90°, BC=10, ∠A=30°, what is the length of AC? | 10√{3} | NULL | free_form |
geo755 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/755.png | As shown in the figure, BD is the angle bisector of the equilateral triangle △ABC. DE is perpendicular to AB, with the foot of the perpendicular at point E. The perpendicular bisector of segment BC intersects BD at point P, with the foot of the perpendicular at F. If PF = 2, then the length of DE is () | 3 | NULL | free_form |
geo756 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/756.png | As shown in the figure, it is a part of the roof truss design. Point D is the midpoint of the inclined beam AB. The columns BC and DE are perpendicular to the horizontal beam AC. Given AB = 6m and ∠A = 30°, what is the length of DE? | 1.5m | NULL | free_form |
geo757 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/757.png | As shown in the figure, tree AB is perpendicular to the ground. To measure the height of the tree, Xiaoming is at point C and measures ∠ACB = 15°. He then walks 20 meters along the direction of CB to reach point D and measures ∠ADB = 30°. What is the height of the tree that Xiaoming calculates? | 10米 | NULL | free_form |
geo758 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/758.png | As shown in the figure, △ABC is an equilateral triangle, point D is the midpoint of AC, DE is perpendicular to BC, and CE = 3. What is the length of AB? | 12 | NULL | free_form |
geo759 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/759.png | As shown in the figure, a road is being constructed along the direction of AC. To speed up the construction progress, work needs to be done simultaneously on the other side of the hill. From a point B on AC, take ∠ABD=150°, BD=500 meters, and ∠D=60°. To ensure that points A, C, and E are in a straight line, what is the distance from point D to the excavation point E? | 250米 | NULL | free_form |
geo760 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/760.png | As shown in the figure, in the right triangle ABC, ∠C=90°, ∠ABC=30°, and AB=16. The triangle ABC is translated to the right along CB to obtain triangle DEF. If the area of quadrilateral ABED is equal to 32, then the translation distance is equal to () | 4 | NULL | free_form |
geo761 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/761.png | As shown in the figure, the side length of square ABCD is 8. M is on DC, and DM = 2. N is a moving point on AC. What is the minimum value of DN + MN? | 10 | NULL | free_form |
geo762 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/762.png | As shown in the figure, the shepherd's home is at point B. The distances from points A and B to the riverbank, AC and BD, are 500m and 300m respectively, and the distance between points C and D is 600m. At dusk, the shepherd leads the cattle from point A to the river to drink water and then returns home. What is the minimum distance the shepherd has to walk? | 1000m | NULL | free_form |
geo763 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/763.png | As shown in the figure, in the equilateral triangle △ABC, E is the midpoint of side AC, AD is the median on side BC, and P is a moving point on AD. If AD = 5, then the minimum value of EP + CP is () | 5 | NULL | free_form |
geo764 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/764.png | As shown in the figure, the perimeter of △ABC is 32. Points D and E are both on side BC. The bisector of ∠ABC is perpendicular to AE, with the foot of the perpendicular being Q. The bisector of ∠ACB is perpendicular to AD, with the foot of the perpendicular being P. If BC = 12, what is the length of PQ? | 4 | NULL | free_form |
geo765 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/765.png | As shown in the figure, in the right triangle ABC, ∠ACB=90°, ∠A=30°, D, E, and F are the midpoints of AB, AD, and AC respectively. If CB=4, what is the length of EF? | 2 | NULL | free_form |
geo766 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/766.png | As shown in the figure, in △ABC, ∠C=90°, E is a point on the extension of CA, F is a point on CB, AE=12, BF=8, points P, Q, and D are the midpoints of AF, BE, and AB respectively. What is the length of PQ? | 2√{13} | NULL | free_form |
geo767 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/767.png | As shown in the figure, m ∥ n, point A is on line n, and the arc with center A intersects lines n and m at points B and C. If ∠CAB = 30°, then the measure of ∠ABC is () | 75° | NULL | free_form |
geo768 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/768.png | As shown in the figure, given AB∥CD, AD=CD, ∠1=40°, what is the degree of ∠2? | 70° | NULL | free_form |
geo769 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/769.png | In △ABC, AB=AC, the perpendicular bisector of AB intersects AB and AC at points D and E respectively. The perimeter of △BCE is 8, and AB=5. What is the perimeter of △ABC? | 13 | NULL | free_form |
geo770 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/770.png | As shown in the figure, in △ABC, AB=AC, point E is on side BC, and point D is taken on the extension of segment AC such that CD=CE. Connect DE, and CF is the median of △CDE. If ∠FCE=52°, then the measure of ∠A is () | 28° | NULL | free_form |
geo771 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/771.png | As shown in the figure, AB is the diameter of circle O, ∠ABC=30°, OA=6, then the area of sector AOC is () | 6π | NULL | free_form |
geo772 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/772.png | As shown in the figure, circles A, B, and C do not intersect with each other, and each has a radius of 0.5. What is the area of the shaded region in the figure? | 0.125π | NULL | free_form |
geo773 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/773.png | As shown in the figure, circles A, B, and C do not intersect each other, and the radius of each is 0.5 cm. What is the total area of the three sectors (i.e., the three shaded parts) in the figure? | \frac{1}{8}πcm² | NULL | free_form |
geo774 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/774.png | As shown in the figure, the four vertices of the square MNEF are on a large circle with a diameter of 4. The small circle is tangent to each side of the square. AB and CD are the diameters of the large circle, AB ⊥ CD, and CD ⊥ MN. What is the area of the shaded part in the figure? | π | NULL | free_form |
geo775 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/775.png | As shown in the figure, in △ABC, ∠A=90°, BC=2cm. Two identical circles are externally tangent at points B and C. What is the total area of the shaded sectors in these two circles? | \frac{π}{4}cm^{2} | NULL | free_form |
geo776 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/776.png | As shown in the figure, AB is the diameter of the semicircle, BC is the tangent, BE is the chord, AC intersects the semicircle at point D, and intersects BE at point F. Given that AF = FC, BC = 1/2 AC = 1, then the area of the shaded part in the figure is () | \frac{√{3}}{4} | NULL | free_form |
geo777 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/777.png | As shown in the figure, the incircle of the equilateral triangle △ABC touches side BC at point D. Given that the side length of the equilateral triangle is 12 cm, what is the area of the shaded region in the figure? | 2πm² | NULL | free_form |
geo778 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/778.png | As shown in the figure, PA is tangent to circle O at point A. The radius of circle O is 3, and PO = 6. If the area of the shaded region in the figure is rac{9}{2}√{3}- rac{3}{2}π, then ∠P = () | 30° | NULL | free_form |
geo779 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/779.png | As shown in the figure, in △ABC, ∠C=90°, ∠A=60°, with A as the center and AC as the radius, draw an arc intersecting AB at D. If the area of the sector ACD (shaded part) is 6π cm², then the length of AB is () | 12cm | NULL | free_form |
geo780 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/780.png | As shown in the figure, OAB is a sector with a radius of 6 cm. AC is tangent to arc AB at point A and intersects the extension of OB at point C. If the length of arc AB is 3 cm and AC = 4 cm, what is the area of the shaded region in the figure? | 3cm² | NULL | free_form |
geo781 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/781.png | As shown in the figure, the slope AB of a certain hillside is 200 meters, and the slope angle ∠BAC is 30°. What is the height BC of this hillside? | 100米 | NULL | free_form |
geo782 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/782.png | As shown in the figure, a sea ship is located at point A, which is 60 nautical miles away from lighthouse P in the direction of 30° north by east. It sails southward for a period of time and reaches point B, which is in the direction of 45° south by east from lighthouse P. At this time, the distance between the sea ship at point B and lighthouse P is () | 30√{2}海里 | NULL | free_form |
geo783 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/783.png | At 9:00 AM, a boat departs from point A, traveling due east at a speed of 40 nautical miles per hour, and reaches point B at 9:30 AM (as shown in the diagram). From points A and B, the island M is observed at bearings of 45° northeast and 15° northeast, respectively. What is the distance between the boat at point B and the island M? | 20√{2}海里 | NULL | free_form |
geo784 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/784.png | As shown in the figure, at 8:00 AM, a ship departs from point A (60 nautical miles/hour) heading due east. At 8:30 AM, it reaches point B. It is measured that the small island M is 45° northeast of point A and 30° northeast of point B. What is the distance BM? | 30√{2}海里 | NULL | free_form |
geo785 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/785.png | The three views of a triangular prism are shown in the figure. In △EFG, EF=8cm, EG=12cm, ∠EGF=30°, then what is the length of AB? | 6 | NULL | free_form |
geo786 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/786.png | As shown in the figure, in circle O, chords AB and CD intersect at the midpoint E of AB. Connect AD and extend it to point F such that DF = AD. Connect BC and BF. If \(\frac{BE}{FB} = \frac{5}{8}\), then the value of \(\frac{CB}{AD}\) is () | \frac{5}{4} | NULL | free_form |
geo787 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/787.png | As shown in the figure, in parallelogram ABCD, diagonals AC and BD intersect at point O. On the extension of DC, take a point E and connect OE, which intersects BC at point F. Given that AB=4, BC=6, and CE=2, what is the length of CF? | 1.5 | NULL | free_form |
geo788 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/788.png | As shown in the figure, in △ABC, DE is parallel to BC, and DE intersects AB and AC at points D and E, respectively. If EC = 1 and AC = 3, what is the value of DE:BC? | \frac{2}{3} | NULL | free_form |
geo789 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/789.png | As shown in the figure, in △ABC, D is the midpoint of AB, and DE∥BC. If the area of △ADE is 3, then the area of △ABC is () | 12 | NULL | free_form |
geo790 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/790.png | As shown in the figure, ⊙O is the circumcircle of △ABC. It is known that AD bisects ∠BAC and intersects ⊙O at point D. Given that AD = 5 and BD = 2, find the length of DE. | \frac{4}{5} | NULL | free_form |
geo791 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/791.png | As shown in the figure, in △ABC, points D and E are points on AC and AB respectively, and \(\frac{AD}{AB} = \frac{AE}{AC} = \frac{1}{2}\). If the area of △ADE is 1 cm², then the area of quadrilateral EBCD is () cm². | 3 | NULL | free_form |
geo792 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/792.png | As shown in the figure, in △ABC, points D and E are on AB and AC respectively, and DE∥BC. If AE:EC=2:3 and AD=6, then the length of AB is () | 15 | NULL | free_form |
geo793 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/793.png | As shown in the figure, in the right triangle ABC, ∠C=90°, AB=10, AC=8, E is a point on AC, AE=5, ED⊥AB, and the foot of the perpendicular is point D. What is the length of AD? | 4 | NULL | free_form |
geo794 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/794.png | As shown in the figure, points D and E are on AB and AC respectively, and ∠B = ∠AED. If DE = 4, AE = 5, and BC = 8, then the length of AB is () | 10 | NULL | free_form |
geo795 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/795.png | As shown in the figure, in △ABC, \(\frac{AD}{DB} = \frac{AE}{EC} = \frac{1}{2}\). If the area of △ADE is 1, then the area of quadrilateral DBCE is () | 8 | NULL | free_form |
geo796 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/796.png | As shown in the figure, points D and E are on line segments AB and AC respectively, and ∠ABC = ∠AED. If DE = 4, AE = 5, and BC = 8, what is the length of AB? | 10 | NULL | free_form |
geo797 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/797.png | As shown in the figure, in △ABC, DE∥BC. If AD=1 and DB=2, then the value of \frac{DE}{BC} is () | \frac{1}{3} | NULL | free_form |
geo798 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/798.png | As shown in the figure, in the square ABCD, E is the midpoint of side AB, and G and F are points on sides AD and BC, respectively. If AG=1, BF=2, and ∠GEF=90°, then the length of GF is () | 3 | NULL | free_form |
geo799 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/799.png | As shown in the figure, D and E are points on the sides AB and AC of triangle △ABC, respectively. ∠1 = ∠B, AE = EC = 4, BC = 10, AB = 12. What is the ratio of the perimeters of △ADE and △ACB? | \frac{1}{3} | NULL | free_form |
geo800 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/800.png | As shown in the figure, squares ABCD and CEFG with side lengths of 2 and 6 respectively are placed side by side. Connect BD and extend it to intersect EG at point T and intersect FG at point P. What is the length of GT? | 2√{2} | NULL | free_form |
geo801 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/801.png | As shown in the figure, in △ABC, D and E are the midpoints of AB and AC, respectively. If the area of △ABC is S_{△ABC} = 36 cm², then the area of △ADE, S_{△ADE}, is () | 9 | NULL | free_form |
geo802 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/802.png | As shown in the figure, the two diagonals of quadrilateral ABCD intersect at point P. Given that ∠ADB = ∠BCA, DC = AP = 6, and DP = 3, find the length of AB. | 12 | NULL | free_form |
geo803 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/803.png | As shown in the figure, it is a schematic diagram of the cross-section of a reservoir dam. Among them, AB and CD respectively represent the horizontal lines of the upper and lower surfaces of the reservoir. ∠ABC=120°, and the length of BC is 100m. What is the height h of the reservoir dam? | 50√{3}m | NULL | free_form |
geo804 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/804.png | As shown in the figure, AB is a vertical utility pole standing on a slope with a slope angle of 30°. When the sunlight forms a 60° angle with the horizontal line, the length of the shadow BC of the utility pole is 4 meters. What is the height of the utility pole AB? | 8米 | NULL | free_form |
geo805 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/805.png | As shown in the figure, in △ABC, points D and E are on AB and AC respectively, and DE ∥ BC. AD = CE. If AB:AC = 3:2 and BC = 10, then the length of DE is () | 4 | NULL | free_form |
geo806 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/806.png | As shown in the figure, in an equilateral triangle △ABC with a side length of 9, BD=3, and ∠ADE=60°, what is the length of AE? | 7 | NULL | free_form |
geo807 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/807.png | As shown in the figure, given AB ∥ CD, AD intersects BC at point P, AB = 2, CD = 3, BC = 6, then the length of BP is equal to () | \frac{12}{5} | NULL | free_form |
geo808 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/808.png | As shown in the figure, in the parallelogram ABCD, E is the midpoint of side DC, and AE intersects BD at point Q. If the area of △DQE is 9, then the area of △AQB is () | 36 | NULL | free_form |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.