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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geo609 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/609.png | As shown in the figure, in △ABC, points D and E are on sides AB and AC respectively, and DE ∥ BC. If AD:DB = 3:2 and AE = 6, then what is the length of EC? | B | ['10', '4', '15', '9'] | 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 |
geo611 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/611.png | As shown in the figure, given that AD∥BE∥CF and \( \frac{AB}{BC} = \frac{2}{3} \), with DE = 3, find the length of DF. | D | ['2', '4.5', '3', '7.5'] | 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 |
geo613 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/613.png | As shown in the figure, in △ABC, point D is on segment BC, ∠B = ∠DAC, AC = 8, BC = 16, then CD() | A | ['4', '6', '8', '10'] | multi_choice |
geo614 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/614.png | As shown in the figure, points D, E, and F are on the sides of triangle ABC, and DE is parallel to BC, DF is parallel to AC. If AE:EC = 1:2 and BC = 12, then the length of DE is () | D | ['1', '2', '3', '4'] | multi_choice |
geo615 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/615.png | As shown in the figure, D and E are points on sides AB and AC of triangle △ABC, respectively. Given that ∠ADE = ∠ACB, AD = 2, AB = 6, and AC = 4, what is the length of AE? | C | ['1', '2', '3', '4'] | multi_choice |
geo616 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/616.png | As shown in the figure, in △ABC, points D and E are on sides AB and AC respectively, and DE ∥ BC. Given that AE = 6 and rac{AD}{DB} = rac{3}{4}, what is the length of AC? | C | ['8', '21', '14', '7'] | multi_choice |
geo617 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/617.png | As shown in the figure, given that l_{1}∥l_{2}∥l_{3}, AB=3, DE=2, EF=4, what is the length of AC? | B | ['6', '9', '3', '4'] | multi_choice |
geo618 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/618.png | As shown in the figure, lines a, b, and c are parallel to each other. Lines m and n intersect lines a, b, and c at points A, B, C, D, E, and F respectively. If AB = 2 and CB = DE = 3, then the length of segment EF is () | C | ['\\frac{2}{7}', '4', '\\frac{9}{2}', '5'] | multi_choice |
geo619 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/619.png | As shown in the figure, in △ABC, points D and E are on sides AB and AC respectively, and DE ∥ BC. If AE:EC = 3:1 and AD = 6, then BD equals () | A | ['2', '4', '6', '8'] | multi_choice |
geo620 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/620.png | As shown in the figure: In △ABC, DE∥BC, AD=5, BD=10, AE=3. What is the value of AC? | A | ['9', '6', '3', '4'] | multi_choice |
geo621 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/621.png | As shown in the figure, in △ABC, DE∥BC, DE=2, AD=4, DB=6, then the length of BC is () | D | ['2', '3', '4', '5'] | multi_choice |
geo622 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/622.png | As shown in the figure, in the parallelogram ABCD, EF is parallel to AB, DE:EA = 1:2, and EF = 4. What is the length of CD? | C | ['\\frac{4}{3}', '8', '12', '16'] | multi_choice |
geo623 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/623.png | As shown in the figure, AD and BC intersect at point O, and AB is parallel to CD. If rac{AO}{OD}= rac{2}{3}, then the value of rac{AB}{CD} is () | C | ['\\frac{2}{5}', '\\frac{3}{2}', '\\frac{2}{3}', '\\frac{4}{9}'] | multi_choice |
geo624 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/624.png | As shown in the figure, l1∥l2∥l3, AB=3, BC=2, EF=3, what is the length of DF? | D | ['3', '5.5', '6.5', '7.5'] | multi_choice |
geo625 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/625.png | As shown in the figure, in △ABC, points D and E are on sides AB and AC respectively, and DE ∥ BC. Given that AE = 9 and rac{AD}{BD} = rac{3}{4}, find the length of EC. | C | ['4.5', '8', '12', '14'] | multi_choice |
geo626 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/626.png | As shown in the figure, the lines l_{1}∥l_{2}∥l_{3} are parallel, and they intersect lines a and b at points A, B, C, D, E, and F respectively. If AB=2, BC=3, and DE=1, then what is the length of EF? | B | ['\\frac{2}{3}', '\\frac{3}{2}', '6', '\\frac{1}{6}'] | multi_choice |
geo627 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/627.png | As shown in the figure, given that lines a ∥ b ∥ c, lines m and n intersect a, b, and c at points A, C, E, B, D, and F respectively. If AC = 4, CE = 6, and BD = 3, what is the value of DF? | B | ['4', '4.5', '5', '5.5'] | multi_choice |
geo628 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/628.png | As shown in the figure, D is the midpoint of side BC of triangle △ABC, and \(\frac{AE}{BE}=\frac{1}{3}\). Find the value of \(\frac{AF}{FC}\). | B | ['\\frac{1}{2}', '\\frac{1}{3}', '\\frac{1}{4}', '\\frac{1}{5}'] | multi_choice |
geo629 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/629.png | As shown in the figure, L_{1}∥L_{2}∥L_{3}, AB=4, DE=3, EF=6, what is the length of BC? | C | ['4', '6', '8', '10'] | multi_choice |
geo630 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/630.png | In triangle ABC, DE is parallel to BC, DE intersects AB at D and intersects AC at E. If AE = 3, EC = 5, and DE = 6, what is the length of BC? | B | ['10', '16', '12', '\\frac{18}{5}'] | multi_choice |
geo631 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/631.png | As shown in the figure: In △ABC, DE∥BC, AD=5, BD=10, AE=3. What is the value of CE? | B | ['9', '6', '3', '4'] | multi_choice |
geo632 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/632.png | As shown in the figure, AD is the median of triangle ABC, and E is a point on AD such that AE = \frac{1}{3}AD. CE intersects AB at point F. If AF = 1 cm, then AB = () cm. | C | ['3', '4', '5', '6'] | multi_choice |
geo633 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/633.png | As shown in the figure, in △ABC, points D and E are on sides AB and AC respectively, and DE ∥ BC. Given that AE = 6 and rac{AD}{BD} = rac{3}{4}, find the length of EC. | B | ['4.5', '8', '10.5', '14'] | multi_choice |
geo634 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/634.png | As shown in the figure, BD = CD, AE:DE = 1:2, extend BE to intersect AC at F, and AF = 5cm. What is the length of AC? | B | ['30cm', '25cm', '15cm', '10cm'] | multi_choice |
geo635 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/635.png | As shown in the figure, DE ∥ BC, and DB = AE. If AB = 5 and AC = 10, what is the length of AE? | D | ['2', '2.5', '√{10}', '\\frac{10}{3}'] | multi_choice |
geo636 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/636.png | As shown in the figure, given that AB ∥ CD, AD intersects BC at point P, AB = 4, CD = 6, AP = 5, then the length of AD is equal to () | A | ['12.5', '10', '9', '7.5'] | multi_choice |
geo637 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/637.png | As shown in the figure, lines AB ∥ CD ∥ EF. If AC = 3 and CE = 4, then the value of \( \frac{BD}{BF} \) is () | C | ['\\frac{3}{4}', '\\frac{4}{3}', '\\frac{3}{7}', '\\frac{4}{7}'] | multi_choice |
geo638 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/638.png | As shown in the figure, △ABC is similar to △DEF with a similarity ratio of 1:2. If BC = 1, then the length of EF is () | B | ['1', '2', '3', '4'] | multi_choice |
geo639 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/639.png | As shown in the figure, in the square ABCD, E is a point on the side CD, and F is a point on the segment AE. If △ADE is similar to △BFA, AE=4, BF=3, then the area of the square is () | A | ['12', '8', '6', '2√{6}'] | multi_choice |
geo640 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/640.png | As shown in the figure, △OED is similar to △OCB, and OE = 6, EC = 21. What is the similarity ratio between △OCB and △OED? | B | ['\\frac{3}{7}', '\\frac{5}{2}', '\\frac{8}{5}', '\\frac{3}{5}'] | multi_choice |
geo641 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/641.png | As shown in the figure, the area of △ABC is 12. Points D and E are the midpoints of sides AB and AC, respectively. What is the area of quadrilateral BCED? | D | ['6', '7', '8', '9'] | multi_choice |
geo642 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/642.png | As shown in the figure, lines a, b, and c are parallel to each other. Lines m and n intersect these three lines at points A, B, C and points D, E, F respectively. If AB = 4, BC = 6, and DE = 3, what is the length of DF? | C | ['4.5', '2', '7.5', '6.5'] | multi_choice |
geo643 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/643.png | As shown in the figure, AC ∥ BD, lines l1 and l2 intersect these two parallel lines at points A, B, and points C, D respectively. l1 and l2 intersect at point E. If rac{AE}{BE}= rac{1}{2}, then the value of rac{CE}{CD} is () | B | ['\\frac{1}{2}', '\\frac{1}{3}', '\\frac{2}{3}', '2'] | multi_choice |
geo644 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/644.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 () | A | ['30°', '40°', '50°', '60°'] | multi_choice |
geo645 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/645.png | As shown in the figure, a person starts from point A, moves forward 8 meters, then turns right 60°, moves forward another 8 meters, and then turns right 60° again. If he continues to walk in this manner, how far will he have walked when he first returns to the starting point A? | D | ['24m', '32m', '40m', '48m'] | multi_choice |
geo646 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/646.png | As shown in the figure, a cargo ship sails from point A to point C in the direction of 45° north-east. At point C, it changes its course and sails to point B. At this time, it is observed that point C is located 63° north-west of point B. What is the degree of angle ∠C? | B | ['99°', '108°', '118°', '128°'] | multi_choice |
geo647 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/647.png | As shown in the figure, in △CEF, ∠E=80°, ∠F=50°, AB∥CF, AD∥CE, connect BC and CD, then the degree of ∠A is () | B | ['45°', '50°', '55°', '80°'] | multi_choice |
geo648 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/648.png | As shown in the figure, C and D are two points on the line segment AB. If BC = 6 cm, BD = 10 cm, and D is the midpoint of AC, then the length of AC is () | C | ['2cm', '4cm', '8cm', '13cm'] | multi_choice |
geo649 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/649.png | As shown in the figure, in △ABC, AB=AC, M and N are the midpoints of AB and AC respectively, D and E are points on BC, and DN and EM are connected. If AB=5cm, BC=8cm, and DE=4cm, then the area of the shaded part in the figure is () | B | ['1cm2', '1.5cm2', '2cm2', '3cm2'] | multi_choice |
geo650 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/650.png | As shown in the figure, in △ABC, M is the midpoint of BC, MI is parallel to CA, and MI intersects the angle bisector AI of ∠A at point I. If AB=10 and AC=16, what is the length of MI? | A | ['3', '\\frac{7}{2}', '4', '\\frac{9}{2}'] | multi_choice |
geo651 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/651.png | As shown in the figure, a set square with a 60° angle is placed between two parallel lines. It is known that the distance between the parallel lines is 12 cm, and the shortest side of the set square forms a 45° angle with the parallel lines. What is the length of the hypotenuse of the set square? | D | ['12cm', '12√{2}cm', '24cm', '24√{2}cm'] | multi_choice |
geo652 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/652.png | As shown in the figure, AB ⊥ BC, CD ⊥ BC, AD ∥ BC. If AB = 3 cm and AD = 4 cm, what is the length of BC? | B | ['3cm', '4cm', '3cm或4cm', '不确定'] | multi_choice |
geo653 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/653.png | As shown in the figure, AB ∥ CD, and EMNF is a broken line between the straight lines AB and CD. If ∠1 = 40°, ∠2 = 60°, and ∠3 = 70°, then the degree of ∠4 is () | B | ['55°', '50°', '40°', '30°'] | multi_choice |
geo654 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/654.png | As shown in the figure: AB ∥ CD, the line MN intersects AB at E, and a line HE is drawn through point E perpendicular to MN. Given that ∠1 = 130°, what is the value of ∠2? | B | ['50°', '40°', '30°', '60°'] | multi_choice |
geo655 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/655.png | As shown in the figure, in △ABC, ∠ACB=90°, ∠A=30°, BC=4cm, point D is the midpoint of AB, then CD=() | B | ['3cm', '4cm', '5cm', '6cm'] | multi_choice |
geo656 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/656.png | As shown in the figure, in △ABC, ∠C=80°, if ∠C is cut off along the dashed line in the figure, then ∠1 + ∠2 = () | C | ['270°', '250°', '260°', '240°'] | multi_choice |
geo657 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/657.png | As shown in the figure, ∠1 + ∠2 = 180°, ∠3 = 108°, then the degree of ∠4 is () | A | ['72°', '80°', '82°', '108°'] | multi_choice |
geo658 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/658.png | As shown in the figure, AD is the bisector of ∠EAC, AD ∥ BC, and ∠B = 30°. What is the measure of ∠C? | C | ['50°', '40°', '30°', '20°'] | multi_choice |
geo659 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/659.png | As shown in the figure, a set square is placed as shown, ∠COD=20°, then the degree of ∠AOB is () | C | ['140°', '150°', '160°', '170°'] | multi_choice |
geo660 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/660.png | As shown in the figure, in △ABC, AB=AC, ∠A=30°, the perpendicular bisector of AB intersects AC at point D. What is the measure of ∠CBD? | B | ['30°', '45°', '50°', '75°'] | multi_choice |
geo661 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/661.png | As shown in the figure, AB ∥ CD, AE bisects ∠CAB and intersects CD at point E. If ∠C = 70°, then ∠AED = () | B | ['55°', '125°', '135°', '140°'] | multi_choice |
geo662 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/662.png | As shown in the figure, AB is the diameter of circle O, and CD is a chord of circle O. If ∠ACD = 30°, then what is ∠BAD? | C | ['30°', '50°', '60°', '70°'] | multi_choice |
geo663 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/663.png | As shown in the figure, in △ABC, ∠ACB=90°, CD∥AB, ∠ACD=35°, then the degree of ∠B is () | C | ['35°', '45°', '55°', '145°'] | multi_choice |
geo664 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/664.png | As shown in the figure, given that AB∥CD∥EF and FC bisects ∠AFE, with ∠C=25°, what is the degree of ∠A? | D | ['25°', '35°', '45°', '50°'] | multi_choice |
geo665 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/665.png | As shown in the figure, given that AB ∥ CD and ∠1 = 70°, what is the measure of ∠2? | D | ['60°', '70°', '80°', '110°'] | multi_choice |
geo666 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/666.png | As shown in the figure, m ∥ n, line l intersects m and n at points A and B respectively, AC ⊥ AB, AC intersects line n at point C. If ∠1 = 35°, then ∠2 equals () | C | ['35°', '45°', '55°', '65°'] | multi_choice |
geo667 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/667.png | As shown in the figure, AB ∥ CD, CB ∥ DE, if ∠B = 72°, then the degree of ∠D is () | C | ['36°', '72°', '108°', '118°'] | multi_choice |
geo668 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/668.png | As shown in the figure, AB is the diameter of the semicircle, point D is the midpoint of arc AC, and ∠ABC = 50°. What is ∠DAB equal to? | B | ['60°', '65°', '70°', '75°'] | multi_choice |
geo669 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/669.png | As shown in the figure, AB ∥ CD, ∠1 = 50°, ∠2 = 110°, then ∠3 = () | A | ['60°', '50°', '70°', '80°'] | multi_choice |
geo670 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/670.png | As shown in the figure, △ABE is translated 2 cm to the right to obtain △DCF. If the perimeter of △ABE is 16 cm, what is the perimeter of quadrilateral ABFD? | C | ['16cm', '18cm', '20cm', '21cm'] | multi_choice |
geo671 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/671.png | As shown in the figure, in △ABC, AB=AC=8, BC=5, the perpendicular bisector of AB intersects AC at D. What is the perimeter of △BCD? | A | ['13', '15', '18', '21'] | multi_choice |
geo672 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/672.png | As shown in the figure, line AB is parallel to line CD, point E is a point on BC, and AE is connected. If ∠DCB = 35°, ∠EAB = 23°, then what is the degree of ∠AEC? | A | ['58°', '45°', '23°', '60°'] | multi_choice |
geo673 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/673.png | As shown in the figure, BO bisects ∠ABC, CO bisects ∠ACB, and BO = CO. If ∠BOC = 100°, then ∠BAO equals () | A | ['10°', '20°', '30°', '40°'] | multi_choice |
geo674 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/674.png | As shown in the figure, in △ABC, AC=BC, ∠C=90°, AD bisects ∠CAB and intersects BC at D, DE is perpendicular to AB at point E, and AC=7cm. Then DE+BD equals () | A | ['7cm', '6cm', '5cm', '4cm'] | multi_choice |
geo675 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/675.png | As shown in the figure, OA is perpendicular to OB. If ∠1 = 40°, then the measure of ∠2 is () | C | ['20°', '40°', '50°', '60°'] | multi_choice |
geo676 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/676.png | As shown in the figure, AB is the diameter of circle O, ∠CBA=30°, then ∠BAC=() | D | ['30°', '70°', '90°', '60°'] | multi_choice |
geo677 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/677.png | As shown in the figure, place the right-angle vertex of a right-angled triangle on one side of a ruler. If ∠1 = 35°, then ∠2 equals () | C | ['35°', '45°', '55°', '65°'] | multi_choice |
geo678 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/678.png | As shown in the figure, points A, B, and C are on circle O, and ∠AOC = 100°. What is the measure of ∠ABC? | D | ['140°', '110°', '120°', '130°'] | multi_choice |
geo679 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/679.png | Place a right-angled triangle as shown in the figure, so that the right-angled side of the triangle containing the 60° angle coincides with one of the right-angled sides of the triangle containing the 45° angle. Then the measure of ∠1 is () | C | ['45°', '60°', '75°', '85°'] | multi_choice |
geo680 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/680.png | As shown in the figure, in △ABC, AB=AC, the perpendicular bisector of AB, DE, intersects AC at point D and intersects AB at point E. If BC=10 and the perimeter of △DBC is 22, then AB=() | B | ['10', '12', '14', '16'] | multi_choice |
geo681 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/681.png | As shown in the figure, points A, B, and C are three points on circle O. Given that ∠ACB = 50°, what is the measure of ∠AOB? | C | ['90°', '95°', '100°', '120°'] | multi_choice |
geo682 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/682.png | As shown in the figure, AB is the diameter of circle O. If ∠BAC = 30°, then what is the degree of ∠D? | C | ['30°', '45°', '60°', '75°'] | multi_choice |
geo683 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/683.png | As shown in the figure, PA, PB, and CD are tangent to circle O at points A, B, and E respectively. CD intersects PA and PB at points C and D. If ∠P = 40°, then the sum of ∠PAE and ∠PBE is () degrees. | D | ['50°', '62°', '66°', '70°'] | multi_choice |
geo684 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/684.png | As shown in the figure, AE, AD, and BC are tangent to circle O at points E, D, and F respectively. If AD = 20, then the perimeter of triangle ABC is () | C | ['20', '30', '40', '50'] | multi_choice |
geo685 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/685.png | A ship is sailing from west to east. At point A, the bearing of the island P is north 75° east. After sailing for 7 nautical miles, at point B, the bearing of the island P is north 60° east. What is the distance BP between the ship and the island P at this time? | A | ['7海里', '14海里', '3.5海里', '4海里'] | multi_choice |
geo686 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/686.png | Fold △ABC along a line parallel to BC, such that point A falls onto point A'. Given that ∠C = 120° and ∠A = 26°, what is the measure of ∠A'DB? | D | ['100°', '104°', '108°', '112°'] | multi_choice |
geo687 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/687.png | As shown in the figure, OA is the radius of circle O, BC is a chord of circle O, and BC is perpendicular to OA. A tangent line DE is drawn from a point D on the extension of BC, with the point of tangency being E. Connect AB and BE. If ∠BDE = 52°, what is the measure of ∠ABE? | D | ['52°', '58°', '60°', '64°'] | multi_choice |
geo688 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/688.png | As shown in the figure, in the right triangle △ACB, ∠C=90°, ∠A=37°, AC=4, what is the approximate length of BC? (sin37°≈0.80, cos37°≈0.60, tan37°≈0.75) | B | ['2.4', '3.0', '3.2', '5.0'] | multi_choice |
geo689 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/689.png | As shown in the figure, lines a and b are intersected by line c, a∥b, ∠2=∠3. If ∠1=80°, then ∠4 equals () | B | ['20°', '40°', '60°', '80°'] | multi_choice |
geo690 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/690.png | As shown in the figure, place the right-angle vertex of the triangle on the straight line b of the two parallel lines a and b. If ∠1 = 40°, then what is the degree of ∠2? | D | ['30°', '45°', '40°', '50°'] | multi_choice |
geo691 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/691.png | As shown in the figure, if D is the midpoint of AB, and E is the midpoint of BC, if AC=8, EC=3, what is AD? | A | ['1', '2', '4', '5'] | multi_choice |
geo692 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/692.png | As shown in the figure, point A is in the direction of 60° west of north from point O, and point B is in the direction of 20° east of south from point O. What is the measure of ∠AOB? | B | ['150°', '140°', '120°', '110°'] | multi_choice |
geo693 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/693.png | As shown in the figure, in quadrilateral ABCD, ∠C = 90°. If ∠C is cut off along the dashed line in the figure, then ∠1 + ∠2 equals () | C | ['90°', '135°', '270°', '315°'] | multi_choice |
geo694 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/694.png | As shown in the figure, in △ABC, the bisectors of ∠ABC and ∠ACB intersect at point O. If ∠BOC = 130°, then the measure of ∠A is () | C | ['100°', '90°', '80°', '70°'] | multi_choice |
geo695 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/695.png | As shown in the figure, AB is a chord of circle O, AB = 6, OD is perpendicular to AB at point D, and intersects at point C. If OB = 5, what is the length of CD? | B | ['0.5', '1', '1.5', '2'] | multi_choice |
geo696 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/696.png | As shown in the figure, the radius of circle O is 5 cm, and the distance from the center of the circle to chord AB is 3 cm. What is the length of chord AB? | B | ['6', '8', '4', '10'] | multi_choice |
geo697 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/697.png | As shown in the figure, chord AB of circle O is 8, OE is perpendicular to AB at point E, and OE is 3. What is the radius of circle O? | D | ['√{7}', '2', '10', '5'] | multi_choice |
geo698 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/698.png | As shown in the figure, △ABC is an inscribed triangle of circle O, with O as the center. OD is perpendicular to AB, and D is the foot of the perpendicular. OE is perpendicular to AC, and E is the foot of the perpendicular. If DE = 3, then what is the length of BC? | A | ['6', '3', '8', '10'] | multi_choice |
geo699 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/699.png | As shown in the figure, given that the radius of circle O is 13 and the length of chord AB is 24, what is the distance from point O to AB? | B | ['6', '5', '4', '3'] | multi_choice |
geo700 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/700.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 in cm? | C | ['2', '3', '4', '6'] | multi_choice |
geo701 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/701.png | As shown in the figure: AB is the diameter of circle O, chord CD is perpendicular to AB at E. If AB = 20 and CD = 16, then the length of segment BE is () | A | ['4', '6', '8', '10'] | multi_choice |
geo702 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/702.png | As shown in the figure, AB is the diameter of circle O, and chord CD is perpendicular to AB with the foot of the perpendicular being P. If CD = 8 and OP = 3, what is the radius of circle O? | C | ['10', '8', '5', '3'] | multi_choice |
geo703 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/703.png | As shown in the figure, AB is the diameter of circle O, and chord CD is perpendicular to AB with the foot of the perpendicular at point E. Connect OC. If AB = 10 and CD = 8, what is the length of AE? | C | ['2.5', '3', '2', '1或者4'] | multi_choice |
geo704 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/704.png | Fold the pentagonal paper ABCDE as shown in the figure, with the crease being AF, and points E and D falling on points E' and D' respectively. Given that ∠AFC = 76°, what is ∠CFD' equal to? | C | ['15°', '25°', '28°', '31°'] | multi_choice |
geo705 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/705.png | As shown in the figure, with vertex C of △ABC as the center, draw an arc with a radius less than the length of CA, intersecting CA at point E and intersecting the extension line CD of BC at point F. Then, with E and F as centers, draw arcs with a radius greater than rac{1}{2} the length of EF, intersecting at point G. Draw ray CG. If ∠A=60° and ∠B=70°, what is the measure of ∠ACG? | C | ['75°', '70°', '65°', '60°'] | multi_choice |
geo706 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/706.png | As shown in the figure, O is a point on the line AB, and ∠1 = 120°. Then, what is ∠COB? | C | ['30°', '45°', '60°', '90°'] | multi_choice |
geo707 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/707.png | As shown in the figure, AB = 10 cm, point O is any point on the line segment AB, C is the midpoint of AO, and D is the midpoint of OB. What is the length of the line segment CD? | C | ['3cm', '4cm', '5cm', '6cm'] | multi_choice |
geo708 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/708.png | As shown in the figure: ∠A=50°, BP bisects ∠ABC, DP bisects ∠ADC, ∠P=20°, then ∠C=() | D | ['20°', '15°', '5°', '10°'] | multi_choice |
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