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geo499 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/499.png | As shown in the figure, in circle O, the central angle ∠BOC = 100°, then ∠BAC = () | A | ['50°', '60°', '70°', '75°'] | multi_choice |
geo500 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/500.png | As shown in the figure, in circle O, arc AB = arc AC, ∠C = 75°, then the degree of ∠A is () | A | ['30°', '35°', '45°', '60°'] | multi_choice |
geo501 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/501.png | As shown in the figure, in circle O, chord AB is parallel to chord CD. If ∠ABC = 30°, then ∠BOD = () | C | ['40°', '50°', '60°', '70°'] | multi_choice |
geo502 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/502.png | As shown in the figure, the diameter BD of circle O is 2, and ∠A = 60°. What is the length of BC? | A | ['√{3}', '2√{3}', '3√{3}', '4√{3}'] | multi_choice |
geo503 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/503.png | As shown in the figure, in circle O, AB = AC, and ∠ADC = 20°, what is the measure of ∠AOB? | A | ['40°', '30°', '20°', '10°'] | multi_choice |
geo506 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/506.png | As shown in the figure, given that points A and B are on circle O, if ∠AOB = 80°, then ∠ACB = () | D | ['80°', '70°', '60°', '40°'] | multi_choice |
geo515 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/515.png | As shown in the figure, A, B, and C are three points on the circle O, and ∠B = 75°. What is the degree measure of ∠AOC? | D | ['120°', '130°', '140°', '150°'] | multi_choice |
geo516 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/516.png | As shown in the figure, AB is the diameter of circle O, and ∠BAC=25°. What is ∠ADC? | D | ['25', '30°', '45°', '65°'] | multi_choice |
geo517 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/517.png | As shown in the figure, in circle O, AB is the diameter, and CD is a chord. If ∠ABD = 55°, then ∠C equals () | B | ['25°', '35°', '45°', '55°'] | multi_choice |
geo518 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/518.png | As shown in the figure, AB is the diameter of circle O, and point C is on circle O. If ∠B = 50°, then the measure of ∠A is () | D | ['80°', '60°', '50°', '40°'] | multi_choice |
geo521 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/521.png | As shown in the figure, it is known that AB and CD are chords of circle O, and AB = CD. If ∠AOB = 70°, what is the measure of ∠CED? | D | ['70°', '60°', '45°', '35°'] | multi_choice |
geo530 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/530.png | As shown in the figure, quadrilateral ABCD is inscribed in circle O. If ∠A = 110°, what is the measure of ∠BOD? | D | ['70°', '110°', '120°', '140°'] | multi_choice |
geo531 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/531.png | As shown in the figure, quadrilateral ABCD is an inscribed quadrilateral in circle O. If ∠AOC = 120°, what is the measure of ∠ABC? | B | ['100°', '120°', '140°', '110°'] | multi_choice |
geo534 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/534.png | As shown in the figure, in the cyclic quadrilateral ABCD, ∠C = 110°, what is the measure of ∠BOD? | A | ['140°', '70°', '80°', '60°'] | multi_choice |
geo535 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/535.png | As shown in the figure, quadrilateral ABCD is inscribed in circle O. If one of its exterior angles ∠DCE is 72°, then ∠BOD is equal to () | A | ['144°', '70°', '110°', '140°'] | multi_choice |
geo537 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/537.png | As shown in the figure, AB is the diameter of circle O, and points C and D are on circle O. If ∠AOD = 30°, what is the degree measure of ∠BCD? | C | ['75°', '95°', '105°', '115°'] | multi_choice |
geo539 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/539.png | As shown in the figure, quadrilateral ABCD is a cyclic quadrilateral, ∠BAD=108°, E is a point on the extension of BC, if CF bisects ∠DCE, then the measure of ∠DCF is () | B | ['52°', '54°', '56°', '60°'] | multi_choice |
geo540 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/540.png | As shown in the figure, points A, B, and C are on circle O. If ∠AOB = 130°, then ∠ACB equals () | B | ['105°', '115°', '125°', '135°'] | multi_choice |
geo543 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/543.png | As shown in the figure, △ABC is an inscribed triangle in circle O, and ∠BOC = 120°. Then, ∠A equals () | B | ['50°', '60°', '55°', '65°'] | multi_choice |
geo547 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/547.png | As shown in the figure, ⊙O is the circumcircle of △ABC. If ∠A = 58°, then the measure of ∠BOC is () | B | ['124°', '116°', '62°', '58°'] | multi_choice |
geo549 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/549.png | As shown in the figure, △ABC is inscribed in circle O. If ∠OBA = 40°, then ∠ACB = () | B | ['40°', '50°', '60°', '80°'] | multi_choice |
geo551 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/551.png | As shown in the figure, the radius of circle O is 1, and △ABC is an inscribed triangle of circle O. Connect OB and OC. If ∠BAC and ∠BOC are supplementary, then the length of chord BC is () | A | ['√{3}', '2√{3}', '3√{3}', '1.5√{3}'] | multi_choice |
geo554 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/554.png | As shown in the figure, △ABC is inscribed in circle O. If ∠ACB = 50°, what is the measure of ∠AOB? | A | ['100°', '90°', '80°', '130°'] | multi_choice |
geo555 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/555.png | As shown in the figure, D is a point on the circumcircle of the equilateral triangle △ABC, and ∠DAC=20°. What is the measure of ∠ACD? | C | ['20°', '30°', '40°', '45°'] | multi_choice |
geo556 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/556.png | As shown in the figure, point P is the circumcenter of triangle ABC. Given that ∠A = 75°, what is the measure of ∠BPC? | A | ['150°', '165°', "142°30'", "127°30'"] | multi_choice |
geo559 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/559.png | As shown in the figure, circle O is tangent to BC at point B, and chord AB is parallel to OC. If ∠C = 40°, what is the measure of ∠AOB? | C | ['60', '70°', '80°', '90°'] | multi_choice |
geo562 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/562.png | As shown in the figure, it is known that AB is a tangent to circle O, point A is the point of tangency, and connecting OB intersects circle O at point C. ∠B = 38°, point D is a point on circle O, connecting CD and AD. Then ∠D equals () | D | ['76°', '38°', '30°', '26°'] | multi_choice |
geo564 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/564.png | As shown in the figure, in circle O, CD is a tangent line, and the point of tangency is D. The line CO intersects circle O at points B and A. If ∠A = 20°, then what is the measure of ∠C? | C | ['25°', '65°', '50°', '75°'] | multi_choice |
geo566 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/566.png | As shown in the figure, AB is the diameter of circle O, CA is tangent to circle O at point A, CO intersects circle O at point D, and BD is connected. If ∠C = 40°, then ∠B equals () | B | ['20°', '25°', '30°', '40°'] | multi_choice |
geo569 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/569.png | As shown in the figure, PA and PB are tangent to circle O at points A and B, respectively. AC is the diameter of circle O, and ∠P = 40°. What is the measure of ∠ACB? | C | ['50°', '60°', '70°', '80°'] | multi_choice |
geo573 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/573.png | As shown in the figure, PA and PB are tangents to circle O, with A and B being the points of tangency. If ∠P = 50°, what is the measure of ∠PAB? | C | ['50°', '60°', '65°', '70°'] | multi_choice |
geo575 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/575.png | As shown in the figure, △ABC is inscribed in circle O, ∠B=60°, CD is the diameter of circle O, the tangent line passing through point A intersects the extension line of CD at point P. If the radius of circle O is 1, then the length of PA is equal to () | B | ['√{2}', '√{3}', '√{5}', '2'] | multi_choice |
geo580 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/580.png | As shown in the figure, AB is a chord of circle O. The extension of AO intersects the tangent to circle O at point B at point C. If ∠C = 40°, what is the measure of ∠ABO? | C | ['50°', '40°', '25°', '20度'] | multi_choice |
geo581 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/581.png | As shown in the figure, AB and AC are two chords of circle O, ∠A = 30°. The tangent line passing through point C intersects the extension of OB at point D. What is the degree of ∠D? | A | ['30°', '35°', '40°', '45°'] | multi_choice |
geo583 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/583.png | As shown in the figure, PA and PB are tangents to circle O at points A and B, respectively. CD is a tangent to circle O, intersecting PA and PB at points C and D. The perimeter of triangle PCD is 36. What is the length of AP? | B | ['12', '18', '24', '9'] | multi_choice |
geo584 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/584.png | As shown in the figure, PA and PB are tangent to circle O at points A and B respectively, and PA = 8. CD is tangent to circle O at point E and intersects PA and PB at points C and D. What is the perimeter of triangle PCD? | B | ['8', '16', '24', '32'] | multi_choice |
geo585 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/585.png | As shown in the figure, AB is a chord of circle O, and BC is tangent to circle O at point B. Connect OA. If ∠ABC = 70°, then ∠A equals () | C | ['10°', '15°', '20°', '30°'] | multi_choice |
geo592 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/592.png | As shown in the figure, the endpoints of a line segment AB of length 10 slide on the positive half-axes of the x-axis and y-axis respectively (the length of the line segment AB remains unchanged). Circle O is tangent to the line segment AB. What is the maximum area of Circle O? | B | ['100π', '25π', '22π', '20π'] | multi_choice |
geo596 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/596.png | As shown in the figure, PA and PB are tangent to circle O at points A and B respectively. If AP = 5, then BP = () | D | ['4', '10', '3', '5'] | multi_choice |
geo598 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/598.png | As shown in the figure, given that the radius of circle O is 5 cm, a straight line is tangent to circle O at point C. If this straight line is translated 2 cm along the direction of CO and intersects circle O at points A and B, what is the length of chord AB? | D | ['2', '3', '5', '8'] | multi_choice |
geo599 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/599.png | As shown in the figure, AB is the diameter of circle O, PA is tangent to circle O at point A, PO intersects circle O at point C, and BC is connected. If ∠P = 36°, then ∠B equals () | A | ['27°', '30°', '36°', '54°'] | multi_choice |
geo603 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/603.png | As shown in the figure, P is a point outside circle O. PA and PB are tangent to circle O at points A and B, respectively. CD is tangent to circle O at point E and intersects PA and PB at points C and D, respectively. If PA = 5, what is the perimeter of triangle PCD? | C | ['5', '8', '10', '12'] | multi_choice |
geo605 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/605.png | As shown in the figure, two concentric circles have the same center O. The chord AB of the larger circle is tangent to the smaller circle at point C. If the radius of the larger circle is 10 cm and the radius of the smaller circle is 6 cm, what is the length of the chord AB? | D | ['2cm', '4cm', '8cm', '16cm'] | multi_choice |
geo607 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/607.png | As shown in the figure, AB is the diameter of the semicircle, with AB = 4. The semicircle rotates 45° clockwise around point B, and point A rotates to position A'. What is the area of the shaded region in the figure? | B | ['π', '2π', '\\frac{π}{2}', '4π'] | multi_choice |
geo608 | /home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/608.png | As shown in the figure, in △ABC, DE∥BC, AD=5, BD=10, DE=6, what is the value of BC? | C | ['6', '12', '18', '24'] | multi_choice |
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 |
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 |
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 |
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 |
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 |
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 |
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 |
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 |
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 |
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 |
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 |
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 |
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 |
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 |
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 |
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 |
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 |
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 |
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 |
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 |
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 |
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 |
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 |
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 |
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 |
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 |
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 |
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 |
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 |
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 |
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 |
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 |
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 |
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 |
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 |
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 |
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 |
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 |
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 |
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 |
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 |
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