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Math

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func633

/home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/633.png

In the rectangular coordinate system xOy, the parabola y=ax²+bx+c is shown in the figure. What is the case of the roots of the equation ax²+bx+c=2? ( )

B

['There are two equal real roots', 'There are two unequal real roots', 'There are real roots', 'There are no real roots']

multi_choice

func758

/home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/758.png

As shown in the figure, in a rectangular coordinate system, the vertices of triangle ABC are A(0, a), B(-1, b), C(2, c), BC passes through the origin O, and CD ⊥ AB with the foot of perpendicular at point D, and AB·CD = 12. What is the value of a?

B. 4

['3', '4', '8', '12']

multi_choice

func948

/home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/948.png

As shown in the figure, given that the line y = x + b intersects with y = kx + 3 at point A, the solution of the system of two linear equations {y = kx + 3, y = x + b} for x and y is ( ).

A

['\\( \\begin{cases} x = 1 \\\\ y = 2 \\end{cases} \\)', '\\( \\begin{cases} x = 2 \\\\ y = 1 \\end{cases} \\)', '\\( \\begin{cases} x = 0 \\\\ y = 3 \\end{cases} \\)', '\\( \\begin{cases} x = 1 \\\\ y = 3 \\end{cases} \\)']

multi_choice

geo8

/home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/8.png

Find x.

2

NULL

free_form

geo24

/home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/24.png

Use parallelogram to, find y.

101

NULL

free_form

geo108

/home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/108.png

Find x. Round to the nearest tenth if necessary.

C

['1.6', '20', '28.1', '31']

multi_choice

geo129

/home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/129.png

Find x.

B

['7', '8', '12', '17']

multi_choice

geo130

/home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/130.png

Find J K.

C

['4', '6', '8', '12']

multi_choice

geo145

/home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/145.png

Find L M.

C

['6', '8.5', '12', '17']

multi_choice

geo146

/home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/146.png

Find the area of the rhombus.

B

['45', '90', '135', '180']

multi_choice

geo150

/home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/150.png

Find x.

D

['10', '20', '25', '30']

multi_choice

geo165

/home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/165.png

In the figure, m \angle 9 = 75. Find the measure of \angle 11.

A

['75', '85', '95', '105']

multi_choice

geo176

/home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/176.png

Find the area of the figure. Round to the nearest tenth if necessary.

B

['121', '165', '209', '330']

multi_choice

geo189

/home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/189.png

\triangle E F G is equilateral, and E H bisects \angle E. Find m \angle 1.

B

['15', '30', '45', '60']

multi_choice

geo190

/home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/190.png

a = 8, b = 15, and c = 17, find \cos A.

D

['0.12', '0.22', '0.44', '0.88']

multi_choice

geo196

/home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/196.png

The radius of \odot P is 5 and P R = 3. Find Q R.

B

['3', '4', '5', '6']

multi_choice

geo198

/home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/198.png

Find the area of the regular polygon. Round to the nearest tenth.

B

['3.5', '6.9', '13.8', '27.6']

multi_choice

geo200

/home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/200.png

Find A P.

B

['8', '8 \\sqrt { 3 }', '16', '24']

multi_choice

geo222

/home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/222.png

In \odot S, L M = 16 and P N = 4 x. What is x?

A

['4', '7', '8', '14']

multi_choice

geo243

/home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/243.png

Find the area of the figure. Round to the nearest tenth if necessary.

B

['8.2', '71.8', '80', '88.2']

multi_choice

geo256

/home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/256.png

Find x.

C

['8', '16', '16 \\sqrt { 3 }', '32']

multi_choice

geo265

/home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/265.png

Find the perimeter of parallelogram A B C D to the nearest tenth.

C

['23.1', '23.9', '34.6', '43.1']

multi_choice

geo270

/home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/270.png

W X Y Z is a square. If W T = 3. Find m \angle W Y X.

B

['30', '45', '60', '75']

multi_choice

geo271

/home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/271.png

In the figure, m \angle 3 = 133. Find m \angle 5.

D

['47', '113', '123', '133']

multi_choice

geo288

/home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/288.png

For the pair of similar figures, use the given areas to find x.

C

['9.0', '11.2', '17.5', '21.9']

multi_choice

geo304

/home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/304.png

As shown in the figure, AC bisects ∠BAD, ∠B = ∠D, AB = 8cm, then AD = ()

B

['6cm', '8cm', '10cm', '4cm']

multi_choice

geo309

/home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/309.png

As shown in the figure, place the right-angle vertex of a triangular ruler on one side of a straight ruler. When ∠2 = 38°, what is ∠1?

A

['52°', '38°', '42°', '60°']

multi_choice

geo310

/home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/310.png

As shown in the figure, AB is the diameter of circle O, and points C and D are on circle O. If ∠C = 20°, then what is the measure of ∠ABD?

B

['80°', '70°', '50°', '40°']

multi_choice

geo312

/home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/312.png

As shown in the figure, in △ABC, ∠A=90°, point D is on side AC, and DE∥BC. If ∠1=35°, then the measure of ∠B is ()

C

['25°', '35°', '55°', '65°']

multi_choice

geo313

/home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/313.png

As shown in the figure, in △ABC, AC = 4 cm, the perpendicular bisector of segment AB intersects AC at point N, and the perimeter of △BCN is 7 cm. What is the length of BC?

C

['1cm', '2cm', '3cm', '4cm']

multi_choice

geo314

/home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/314.png

As shown in the figure, quadrilateral ABCD is an inscribed quadrilateral of circle O. If ∠DAB = 60°, then the measure of ∠BCD is ()

D

['60°', '90°', '100°', '120°']

multi_choice

geo316

/home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/316.png

As shown in the figure, points A, B, and C are on circle O, and ∠A = 60°. What is ∠BOC?

C

['60°', '90°', '120°', '135°']

multi_choice

geo322

/home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/322.png

As shown in the figure, in circle O, chords AB and CD intersect at point M. Given ∠A = 45° and ∠AMD = 75°, what is the measure of ∠B?

C

['15°', '25°', '30°', '75°']

multi_choice

geo324

/home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/324.png

As shown in the figure, line a is parallel to line b, and ∠1 = 55°. What is ∠2?

C

['35°', '45°', '55°', '65°']

multi_choice

geo327

/home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/327.png

As shown in the figure, in △ABC, ∠CAB=70°. Rotate △ABC counterclockwise around point A to the position of △AB'C', making CC'∥AB. What is the degree of ∠BAB'?

C

['70°', '35°', '40°', '50°']

multi_choice

geo328

/home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/328.png

As shown in the figure, AB is the diameter of circle O, and quadrilateral ABCD is an inscribed quadrilateral of circle O. Point P is on the extension of BA, and PD is tangent to circle O at point D. If ∠BCD = 120°, then what is the measure of ∠APD?

D

['45°', '40°', '35°', '30°']

multi_choice

geo332

/home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/332.png

As shown in the figure: it is a section of stairs, the height BC is 3m, the hypotenuse AC is 5m. If a carpet is to be laid on the stairs, then at least how much carpet is needed?

C

['5m', '6m', '7m', '8m']

multi_choice

geo334

/home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/334.png

As shown in the figure, given four lines a, b, c, and d, where a∥b and c∥d, and ∠1=110°, what is the value of ∠2?

B

['50°', '70°', '90°', '110°']

multi_choice

geo335

/home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/335.png

As shown in the figure, CD is the diameter of circle O. Given that ∠1 = 30°, what is the value of ∠2?

C

['30°', '45°', '60°', '70°']

multi_choice

geo339

/home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/339.png

As shown in the figure, the diagonals of parallelogram ABCD intersect at point O, and AB = 6. The perimeter of △OCD is 16. What is the sum of AC and BD?

C

['10', '16', '20', '22']

multi_choice

geo346

/home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/346.png

As shown in the figure, line a is parallel to line b, AC is perpendicular to AB, AC intersects line b at point C, and ∠2 = 42°. What is the degree of ∠1?

C

['38°', '42°', '48°', '58°']

multi_choice

geo350

/home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/350.png

As shown in the figure, given that AB ∥ CD and ∠2 = 135°, what is the degree of ∠1?

B

['35°', '45°', '55°', '65°']

multi_choice

geo352

/home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/352.png

As shown in the figure, AB = AC, AD ∥ BC, ∠BAC = 100°, then the degree of ∠CAD is ()

C

['30°', '35°', '40°', '50°']

multi_choice

geo353

/home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/353.png

As shown in the figure, place the right-angle vertex of an isosceles right triangle on one side of a ruler. If ∠1 = 40°, then ∠2 = ()

C

['40°', '45°', '50°', '60°']

multi_choice

geo354

/home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/354.png

As shown in the figure, points A and C to be measured are separated by a pond. Master Li randomly selects a point B outside of AC, connects BA and BC, and takes the midpoints E and F of BA and BC, respectively. The distance between points E and F is measured to be 23 meters. What is the distance between points A and C?

A

['46', '23', '50', '25']

multi_choice

geo357

/home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/357.png

As shown in the figure, a shepherd is herding horses at point A. The shepherd's home is at point B. The distances from A and B to the riverbank, AC and BD, are 500 meters and 700 meters respectively. The distance between points C and D is 1600 meters. Before it gets dark, the shepherd leads the horse from point A to the river to drink water and then returns home. What is the minimum distance the shepherd needs to walk?

C

['2600米', '2300米', '2000米', '1200米']

multi_choice

geo358

/home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/358.png

As shown in the figure, OA is perpendicular to OB. If ∠1 = 42°, then what is the measure of ∠2?

D

['52°', '58°', '42°', '48°']

multi_choice

geo362

/home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/362.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 = 22°, then the measure of ∠2 is ()

B

['30°', '23°', '22°', '15°']

multi_choice

geo365

/home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/365.png

As shown in the figure, a//b, ∠1=65°, ∠2=140°, then ∠3=()

B

['100°', '105°', '110°', '115°']

multi_choice

geo366

/home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/366.png

As shown in the figure, point O is inside triangle ABC, and the distances to the three sides are equal. If ∠A = 60°, then what is the measure of ∠BOC?

B

['135°', '120°', '90°', '60°']

multi_choice

geo369

/home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/369.png

As shown in the figure, points D and E are the midpoints of sides AB and AC of the inscribed equilateral triangle ABC in circle O, respectively. If the radius of circle O is 2, then the length of DE is equal to ()

A

['√{3}', '√{2}', '1', '\\frac{√{3}}{2}']

multi_choice

geo371

/home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/371.png

As shown in the figure, in the right triangle ABC, ∠C=90°, ∠B=25°. With C as the center and the length of CA as the radius, a circle intersects AB at point D. What is the degree measure of arc AD?

B

['25°', '50°', '45°', '30°']

multi_choice

geo372

/home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/372.png

As shown in the figure, the vertices A, B, and D of the parallelogram ABCD are on the circle O, and the vertex C is on the diameter BE of the circle O. Given that ∠ADC = 53°, connect AE. What is the measure of ∠AEB?

A

['37°', '46°', '27°', '63°']

multi_choice

geo375

/home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/375.png

As shown in the figure, points A, B, and C are on circle O. If ∠AOB = 62°, then ∠ACB equals ()

C

['29°', '30°', '31°', '32°']

multi_choice

geo377

/home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/377.png

As shown in the figure, AB is the diameter of circle O, point C is on circle O, CD bisects ∠ACB and intersects circle O at point D. If ∠ABC = 30°, then what is the measure of ∠CAD?

B

['l00°', '105°', '110°', '120']

multi_choice

geo379

/home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/379.png

As shown in the figure, AB is the diameter of circle O, and chord CD is perpendicular to AB at point E. Connect OC and BD. If ∠AOC = 110°, what is the measure of ∠ABD?

C

['35°', '46°', '55°', '70°']

multi_choice

geo380

/home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/380.png

As shown in the figure, ∠A is the inscribed angle of circle O, and ∠A = 40°. What is the degree of ∠OBC?

B

['40°', '50°', '60°', '80°']

multi_choice

geo381

/home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/381.png

As shown in the figure, AB is the diameter of circle O, and points C and D are on circle O. If ∠ACD = 15°, what is the measure of ∠BAD?

A

['75°', '72°', '70°', '65°']

multi_choice

geo384

/home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/384.png

As shown in the figure, given that points A, B, and C are on circle O, and ∠C = 35°, what is the measure of ∠AOB?

B

['75°', '70°', '60°', '35°']

multi_choice

geo385

/home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/385.png

As shown in the figure, points A, B, and C are on circle O. If ∠AOB = 130°, then the measure of ∠C is ()

C

['150°', '130°', '115°', '120°']

multi_choice

geo387

/home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/387.png

As shown in the figure, BC is the diameter of circle O, and points A and D are on circle O. If ∠D = 36°, then what is the degree measure of ∠BCA?

C

['36°', '45°', '54°', '72°']

multi_choice

geo388

/home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/388.png

As shown in the figure, points A, B, and C are on circle O, and D is the midpoint of segment AB. If ∠ACD = 20°, what is the measure of ∠AOB?

C

['60°', '70°', '80°', '90°']

multi_choice

geo389

/home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/389.png

As shown in the figure, points A, B, and C are all on circle O. If ∠BAC = 36°, then the measure of ∠BOC is ()

B

['75°', '72°', '64°', '54°']

multi_choice

geo390

/home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/390.png

As shown in the figure, AB is the diameter of circle O, and C and D are two points on circle O. If ∠AOC = 130°, then what is the measure of ∠D?

C

['65°', '35°', '25°', '15°']

multi_choice

geo392

/home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/392.png

As shown in the figure, in the acute triangle ABC, AD and CE are the altitudes on sides BC and AB, respectively, with the feet of the perpendiculars being D and E, respectively. AD and CE intersect at point O. If ∠B = 60°, then what is the measure of ∠AOE?

A

['60°', '50°', '70°', '80°']

multi_choice

geo394

/home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/394.png

As shown in the figure, the cross-section of a cylindrical drainage pipe is given. It is known that the distance from the center O to the water surface OC is 3 dm, the width of the water surface AB is 8 dm. What is the diameter of the cross-section of the drainage pipe?

B

['16dm', '10dm', '8dm', '6dm']

multi_choice

geo400

/home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/400.png

As shown in the figure, the radius of the base of the cone is 3, and the slant height is 6. What is the lateral surface area?

D

['8π', '6π', '12π', '18π']

multi_choice

geo401

/home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/401.png

A large sunshade umbrella, when opened, can be approximately considered as a conical shape, as shown in the figure. The slant height is 2.5 meters, and the radius of the base is 2 meters. What is the area of the fabric needed to make this sunshade umbrella (excluding seams)?

B

['\\frac{25}{4}π', '5π', '4π', '3π']

multi_choice

geo406

/home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/406.png

A sector of paper with a central angle of 90° and a radius of 16 cm is rolled into a bottomless conical paper hat (seam not considered), as shown in the figure. What is the radius of the base of this paper hat?

B

['8cm', '4cm', '16cm', '2cm']

multi_choice

geo412

/home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/412.png

As shown in the figure, the radius of the base of the cone, OA, is 2, and the slant height, AB, is 3. What is the lateral surface area of this cone?

B

['3π', '6π', '12π', '18π']

multi_choice

geo414

/home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/414.png

As shown in the figure, in the right triangle ABC, ∠C=90°, AB=5, AC=4. If the right triangle ABC is rotated around the line where side AC lies, what is the total surface area of the resulting solid?

C

['15π', '20π', '24π', '36π']

multi_choice

geo415

/home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/415.png

As shown in the figure, an open umbrella can be approximately regarded as a cone. The diameter AC of the circle where the ends of the umbrella ribs (the frame under the fabric that can support the fabric) are located is 12 decimeters, and the length of the umbrella rib AB is 9 decimeters. How much silk fabric is needed to make such an umbrella, at least in square decimeters?

B

['36π', '54π', '27π', '128π']

multi_choice

geo417

/home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/417.png

As shown in the figure, in the right triangle ABC, ∠BAC=90°, AC=4, and BC=5. If the right triangle ABC is rotated around the line AC for one full turn, what is the lateral surface area of the resulting cone?

C

['9π', '12π', '15π', '20π']

multi_choice

geo419

/home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/419.png

As shown in the figure, a sector-shaped piece of paper with a radius of 15 cm is used to form a conical paper tube (with no gaps or overlaps at the joint). The radius of the base of the conical paper tube is 6 cm. What is the area of the sector in cm²?

B

['90', '90π', '180π', '126π']

multi_choice

geo420

/home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/420.png

As shown in the figure, the lower part of the ice cream cone is conical, with the diameter of the base circle being 5 cm and the slant height being 8 cm. What is the area of the wrapping paper for the conical part of the cone (ignoring the seam)?

B

['36πcm^{2}', '20πcm^{2}', '18πcm^{2}', '8πcm^{2}']

multi_choice

geo429

/home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/429.png

As shown in the figure, points A, B, and C are on circle O. If ∠C = 44°, then what is the measure of ∠AOB?

B

['22°', '88°', '66°', '70°']

multi_choice

geo430

/home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/430.png

As shown in the figure, Xiao Liu made a schematic diagram of a kite frame. It is known that BC∥PQ, AB:AP=2:5, and BC=20cm. What is the length of PQ?

B

['45cm', '50cm', '60cm', '80cm']

multi_choice

geo436

/home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/436.png

As shown in the figure, two adjacent poles are fixed to the ground with steel cables. One pole's steel cable is tied at a point 4 meters above the ground, and the other pole's steel cable is tied at a point 6 meters above the ground. At what height above the ground does the point P, where the two steel cables intersect, lie?

A

['2.4m', '2.6m', '2.8m', '3m']

multi_choice

geo439

/home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/439.png

As shown in the figure, Xiao Ming designed a schematic diagram to measure the height of an ancient city wall CD using light. If the distance between the mirror P and the ancient city wall is PD=12 meters, the distance between the mirror P and Xiao Ming is BP=1.5 meters, and Xiao Ming just sees the top point C of the ancient city wall from the mirror. The height of Xiao Ming's eyes from the ground is AB=1.2 meters. What is the height of the ancient city wall?

A

['9.6米', '18米', '8米', '24米']

multi_choice

geo441

/home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/441.png

As shown in the figure, AB is the diameter of circle O, point C is on circle O, and ∠A = 40°. What is the degree of ∠B?

B

['65°', '50°', '130°', '80°']

multi_choice

geo444

/home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/444.png

As shown in the figure, Wang Hua places a plane mirror E on the ground to measure the height of the iron tower AB. The distance between the mirror and the iron tower is EB=20 meters, and the distance between the mirror and Wang Hua is ED=2 meters. When Wang Hua sees the top point A of the iron tower from the mirror, it is known that the height of Wang Hua's eyes from the ground is CD=1.5 meters. What is the height of the iron tower AB?

A

['15米', '米', '16米', '16.5米']

multi_choice

geo448

/home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/448.png

As shown in the figure, the short arm of the railway crossing barrier is 1.25 meters long, and the long arm is 16.5 meters long. When the end of the short arm drops by 0.85 meters, the end of the long arm rises by (ignoring the width of the barrier).

B

['11米', '11.22米', '17米', '10米']

multi_choice

geo452

/home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/452.png

As shown in the figure, there is a point light source S above a plane mirror. If the reflected light of the point light source is seen at point P, and it is measured that AB=10cm, BC=20cm, PC⊥AC, and PC=24cm, what is the distance from the point light source S to the plane mirror, i.e., the length of SA?

B

['11cm', '12cm', '13cm', '14cm']

multi_choice

geo457

/home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/457.png

As shown in the figure, in circle O, chords AB and CD intersect at point P. If ∠ADC = 20°, then ∠B equals ()

A

['20°', '25°', '30°', '35°']

multi_choice

geo459

/home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/459.png

As shown in the figure, in △ABC, ∠B=90°, AB=3, BC=4, then \\cosA equals ()

D

['\\frac{3}{4}', '\\frac{4}{3}', '\\frac{4}{5}', '\\frac{3}{5}']

multi_choice

geo467

/home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/467.png

As shown in the figure, in △ABC, ∠A=90°, AC=9, sinB=0.6, then AB is equal to ()

B

['10', '12', '15', '18']

multi_choice

geo470

/home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/470.png

As shown in the figure, points A, B, and C are all on circle O. If ∠ACB = 48°, then what is the measure of ∠AOB?

A

['96°', '48°', '42°', '24°']

multi_choice

geo471

/home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/471.png

As shown in the figure, in △ABC, ∠C=90°, AC=4, BC=3, then sinA=()

A

['\\frac{3}{5}', '\\frac{4}{5}', '\\frac{5}{3}', '\\frac{3}{4}']

multi_choice

geo472

/home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/472.png

Given that in right triangle ABC, ∠C=90°, sinA=\frac{1}{3}, and BC=2, find AB.

A

['6', '4√{2}', '3', '2√{2}']

multi_choice

geo473

/home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/473.png

As shown in the figure, in △ABC, ∠ACB=90°, ∠A=15°, AB=8, then the value of AC•BC is ()

D

['14', '16√{3}', '4√{15}', '16']

multi_choice

geo475

/home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/475.png

As shown in the figure, in △ABC, ∠C=90°, AB=5, AC=3, then sinB=()

C

['\\frac{3}{4}', '\\frac{4}{3}', '\\frac{3}{5}', '\\frac{4}{5}']

multi_choice

geo476

/home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/476.png

In right triangle △ABC, ∠C=90°, if sinA=rac{3}{5}, then cosB=()

D

['\\frac{5}{3}', '\\frac{4}{5}', '\\frac{3}{4}', '\\frac{3}{5}']

multi_choice

geo477

/home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/477.png

As shown in the figure, △ABC is inscribed in circle O, and AC is the diameter of circle O. Given that ∠ACB = 52°, point D is on segment AC. What is the measure of ∠D?

B

['52°', '38°', '19°', '26°']

multi_choice

geo478

/home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/478.png

As shown in the figure, in the obtuse triangle △ABC, ∠A=30°, what is the value of tanA?

C

['√{3}', '\\frac{√{3}}{2}', '\\frac{√{3}}{3}', '无法确定']

multi_choice

geo480

/home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/480.png

As shown in the figure, in the right triangle BAD, extend the hypotenuse BD to point C, making DC = \frac{1}{2}BD. Connect AC. If tanB = \frac{5}{3}, then the value of tan∠CAD is ()

D

['\\frac{√{3}}{3}', '\\frac{√{3}}{5}', '\\frac{1}{3}', '\\frac{1}{5}']

multi_choice

geo482

/home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/482.png

As shown in the figure, points A, B, C, and D are all on circle O. OB is perpendicular to CD, and ∠BOC = 50°. What is the measure of ∠BAD?

D

['50°', '40°', '30°', '25°']

multi_choice

geo487

/home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/487.png

As shown in the figure, AB is the diameter of circle O, C is a point on circle O, OD is perpendicular to BC at point D, and AC = 8. What is the length of OD?

B

['3', '4', '4.5', '5']

multi_choice

geo489

/home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/489.png

As shown in the figure, the central angle ∠AOB = 60°, then the measure of the inscribed angle ∠ACB is ()

A

['30°', '60°', '90°', '120°']

multi_choice

geo492

/home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/492.png

As shown in the figure, in circle O, arc AB is equal to arc BC, point D is on circle O, and angle CDB is 20°. What is the measure of angle AOB?

B

['35°', '40°', '45°', '50°']

multi_choice

geo496

/home/yz979/scratch/chengye/math/data/original_set/geoset/images/images/496.png

As shown in the figure, ⊙O is the circumcircle of △ABC, ∠A=40°, then ∠OCB equals ()

B

['60°', '50°', '40°', '30°']

multi_choice