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As shown in the figure, AB is the diameter of circle O, points C and D are two points on the circle, and angle AOC = 126.0, then angle CDB = ()
Choices:
A:54°
B:64°
C:27°
D:37° | C |
|
As shown in the figure, AB is the diameter of circle O, points C and D are on circle O, and point C is the midpoint of arc BD, passing point C to draw the perpendicular line EF of AD and it intersects straight line AD at point E, if the radius of circle O is 2.5, the length of AC is 4.0, then the length of CE is ()
Choices:
A:3
B:\frac{20}{3}
C:\frac{12}{5}
D:\frac{16}{5} | C |
|
As shown in the figure, the points A, B, and C are on circle O, and it is known that angle ABC = 130.0, then angle AOC = ()
Choices:
A:100°
B:110°
C:120°
D:130° | A |
|
As shown in the figure, it is known that the radius of circle O is 5.0, the central angles of chords AB and CD are angle AOB, angle COD, and angle AOB is complementary to angle COD, chord CD = 8.0, then the length of chord AB is ()
Choices:
A:6
B:8
C:5√{2}
D:5√{3} | A |
|
As shown in the figure, AB is the diameter of circle O, CD is the chord of circle O, and the extended lines of AB and CD intersect at point E. Given that AB = 2 DE, angle E = 16.0, then the degree of angle ABC is ()
Choices:
A:32°
B:24°
C:16°
D:48° | B |
|
This question examines the theorem of angle of circumference, the key is to answer it based on the relationship between the central angle and the angle of circumference of the same chord. 4.0. As shown in the figure, AB is the diameter of circle O, C is the point on circle O (except A and B), angle AOD = 136.0, then the degree of angle C is ()
Choices:
A:44°
B:22°
C:46°
D:36° | B |
|
As shown in the figure, AB is the diameter of circle O, and points C and D are on circle O. If angle BOD = 130.0, then the degree of angle ACD is ()
Choices:
A:50°
B:30°
C:25°
D:20° | C |
|
Shaoxing is a famous bridge township. As shown in the figure, the distance CD from the top of the round arch bridge to the water surface is 8.0, and the arch radius OC is 5.0, so the width of the water surface AB is ()
Choices:
A:4m
B:5m
C:6m
D:8m | D |
|
As shown in the figure, it is known that angle α = 130.0, then angle β = ()
Choices:
A:30°
B:40°
C:50°
D:65° | B |
|
As shown in the figure, when the width of the water surface AB in the circular bridge hole is 8.0, the arc ACB is exactly a semicircle. When the water surface rises 1.0, the water surface width A′B′ in the bridge hole is ()
Choices:
A:√{15}米
B:2√{15}米
C:2√{17}米
D:不能计算 | B |
|
In the right triangle ABC, angle CAB = 90.0, angle ABC = 72.0, AD is the angle bisector of angle CAB, and the intersection BC is at point D, and crossing point C is the high line CE on the AD side in triangle ACD, then the degree of angle ECD is ()
Choices:
A:63°
B:45°
C:27°
D:18° | C |
|
As shown in the figure, AO is the height of the cone, the bottom radius of the cone OB = 0.7, the length of AB is 2.5, then the length of AO is ()
Choices:
A:2.4
B:2.2
C:1.8
D:1.6 | A |
|
As shown in the figure, in circle O, chord AC and BD intersect at point E, arc AB = arc BC = arc CD, if angle BEC = 110.0, then angle BDC = ()
Choices:
A:35°
B:45°
C:55°
D:70° | A |
|
As shown in the figure, in the sector OAB with a radius of 1.0 and a central angle of 90.0, OA and OB are the diameters respectively as a semicircle, and the area of the shaded part in the figure is ()
Choices:
A:πcm²
B:\frac{2}{3}πcm²
C:\frac{1}{2}cm²
D:\frac{2}{3}cm² | C |
|
Use a sector paper sheet with a central angle of 120.0 and a radius of 6.0 to roll into a conical bottomless paper cap (as shown in the picture), then the bottom perimeter of the paper cap is ()
Choices:
A:2πcm
B:3πcm
C:4πcm
D:5πcm | C |
|
The picture shows a small paper cap with a conical chimney. The length of its generatrix l is 13.0 and its height h is 12.0. The area of paper required to make this paper cap is (the seams are ignored) ()
Choices:
A:60π
B:65π
C:78π
D:156π | B |
|
Use a sector piece of paper with a central angle of 120.0 and a radius of 3.0 to roll into a cone-shaped bottomless paper cap (as shown in the picture), then the height of the paper is ()
Choices:
A:3cm
B:2√{2}cm
C:3√{2}cm
D:4√{2}cm | B |
|
As shown in the figure, the expanded figure of the lateral surface of a cone is a semicircle with a radius of 10.0, then the radius of its bottom is ()
Choices:
A:3
B:4
C:5
D:6 | C |
|
As shown in the figure, use a sector cardboard with a radius of 24.0 to make a conical hat (the seams are ignored). If the radius of the bottom surface of the conical hat is 10.0, then the area of this sector cardboard is ()
Choices:
A:240πcm^{2}
B:480πcm^{2}
C:1200πcm^{2}
D:2400πcm^{2} | A |
|
As shown in the figure, the length of the generatrix of the cone is 5.0, and the length of the height line is 4.0, then the bottom area of the cone is ()
Choices:
A:3πcm^{2}
B:9πcm^{2}
C:16πcm^{2}
D:25πcm^{2} | B |
|
The production process of paper umbrellas in our country is very ingenious. As shown in the figure, whether the umbrella is opened or closed, the handle AP always bisects the angle angle BAC formed by the two ribs in the same plane, and AE = AF, DE = DF, so as to ensure that the umbrella ring can slide along the handle. When a toy umbrella is opened, the BDC is on the same straight line. If AB = 50.0, AD = 14.0, then the area of oil paper required to make such a paper umbrella is (don't remember the seam) ()
Choices:
A:48cm^{2}
B:70πcm^{2}
C:2400πcm^{2}
D:2500πcm^{2} | C |
|
As shown in the figure, a sector with a central angle of 120.0 and a radius of 6.0 encloses the side of a cone (the joints are ignored), then the height of the cone is ()
Choices:
A:6
B:8
C:3√{3}
D:4√{2} | D |
|
As shown in the figure, in Rttriangle ABC, angle ACB = 90.0, AC = 4.0, BC = 3.0, rotate triangle ABC around the line where AC is located to obtain a rotating body, then the lateral area of the rotating body is ()
Choices:
A:12π
B:15π
C:30π
D:60π | B |
|
As shown in the figure, cut a circle and a sector piece of paper on the paper so that it can form a cone model. If the radius of the circle is 1.0 and the central angle of the sector is equal to 90.0, then the radius of the sector is ()
Choices:
A:2
B:4
C:6
D:8
127 | B |
|
As shown in a sector iron sheet OAB, it is known that OA = 30.0, angle AOB = 120.0, the worker master combines OA and OB to form a conical chimney cap (the joints are ignored), then the radius of the bottom circle of the chimney cap is ()
Choices:
A:5cm
B:12cm
C:10cm
D:15cm | C |
|
As shown in the figure, it is known that the radius of the bottom surface of the cone is 6.0, and the length of the generatrix is 10.0, then the lateral area of the cone is ()
Choices:
A:60π
B:80π
C:10π
D:96π | A |
|
Lulu cuts a circle and a sector piece of paper from the paper (as shown in the picture), and uses them to form a cone model. If the radius of the circle is 1.0. The central angle of the sector is equal to 120.0, then the radius of the sector is ()
Choices:
A:√{3}
B:√{6}
C:3
D:6 | C |
|
As shown in the figure, there is a sector with a central angle of 120.0 and a radius of 6.0. If OA and OB are overlapped to form a cone side, the diameter of the bottom of the cone is ()
Choices:
A:2cm
B:4cm
C:3cm
D:5cm | B |
|
As shown in the picture, the length of the generatrix of the cone-shaped tent roof is AB = 10.0, the bottom radius is BO = 5.0, and the lateral area of the cone-shaped tent roof (excluding the seams) is ()
Choices:
A:15πm^{2}
B:30πm^{2}
C:50πm^{2}
D:75πm^{2} | C |
|
As shown in the figure, in circle O, the length of chord AB is 10.0, and the angle of circumference angle ACB = 45.0, then the diameter of the circle AD is ()
Choices:
A:5√{2}
B:10√{2}
C:15√{2}
D:20√{2} | B |
|
As shown in the figure, in triangle ABC. angle C = 90.0, point D is a moving point on BC (point D does not coincide with point C). The circle with CD as the diameter intersects AD at point P. If AC = 6.0. The minimum length of the line segment BP is 2.0. Then the length of AB is ()
Choices:
A:8
B:2√{10}
C:4√{3}
D:2√{13} | D |
|
As shown in the figure, in order to measure the height AB of a pavilion (the distance from the top A to the horizontal ground BD), Xiaoming placed a step DE (DE = BC = 0.6) that is the same height as the pavilion step BC beside the pavilion, find A, B, C Three points are collinear), place a mirror horizontally at point G on the platform, and measure CG = 12.0, and then move back along the straight line CG to point E. At this time, you can see the top A of the pavilion in the mirror, and measure GE = 2.0, Xiaoming's height EF = 1.6, then the height of the pavilion AB is approximately ()
Choices:
A:9米
B:9.6米
C:10米
D:10.2米 | D |
|
As shown in the figure, in order to estimate the width of the Jing River, a target point P is selected on the opposite bank of the Jing River, and points Q and S are taken near the bank, so that the points P, Q, and S are in a straight line, and the straight line PS is perpendicular to the river. Choose an appropriate point T on the straight line a passing point S and perpendicular to PS. The intersection of PT and the straight line b passing point Q and perpendicular to PS is R. If QS = 60.0, ST = 120.0, QR = 80.0, then the width of the river PQ is ()
Choices:
A:40m
B:120m
C:60m
D:180m | B |
|
As shown in the picture, Xiaoying designed a flashlight to measure the height of an ancient city wall. Place a horizontal plane mirror at point P. The light starts from point A and is reflected by the plane mirror and hits the top C of the ancient city wall CD. It is known that AB perpendicular BD, CD perpendicular BD. And it is measured that AB = 1.4, BP = 2.1, PD = 12.0. Then the height of the ancient city wall CD is ()
Choices:
A:6米
B:8米
C:10米
D:12米 | B |
|
As shown in the figure, in circle O, point M is the midpoint of arc AB. Connect MO and extend it to intersect circle O at point N, connect BN, if angle AOB = 140.0, then the degree of angle N is ()
Choices:
A:70°
B:40°
C:35°
D:20° | C |
|
As shown in the figure, in order to measure the degree of tree AB, a certain mathematics learning interest group measured the length of the tree's shadow BC in the sun as 9.0. At the same moment, they also measured the shadow length of Xiaoliang in the sun as 1.5. Knowing that Xiaoliang's height is 1.8, then the height of tree AB is ()
Choices:
A:10.8m
B:9m
C:7.5m
D:0.3m | A |
|
As shown in the picture, it is an ancient masher in the countryside. It is known that the height of the support column AB is 0.3, the length of the pedal DE is 1.0, and the distance from the support point A to the foot D is 0.6. When foot D touches the ground, the head point E rises ()
Choices:
A:0.5米
B:0.6米
C:0.3米
D:0.9米 | A |
|
As shown in the figure, the light source P is directly above the crossbar AB, the shadow of AB under the light is CD, AB parallel CD, AB = 2.0, CD = 5.0, the distance between point P and CD is 3.0, then the distance between AB and CD is ().
Choices:
A:\frac{6}{5}
B:\frac{7}{6}
C:\frac{9}{5}
D:\frac{15}{2} | C |
|
As shown in the figure, Xiaoqiang made a small hole imaging device in which the length of the paper tube is 15.0. He prepared a candle with a length of 20.0. To get an image with a height of 4.0, the distance between the candle and the paper tube should be ()
Choices:
A:60cm
B:65cm
C:70cm
D:75cm | D |
|
As shown in the figure, in a badminton game, Lin Dan, the athlete standing at M in the field, clicks the request from N to point B in the opponent. It is known that the net height OA = 1.52, OB = 4.0, OM = 5.0, then when Lin Dan takes off, the distance from the hitting point to the ground NM = ()
Choices:
A:3.42m
B:1.9m
C:3m
D:3.24m | A |
|
While measuring the height of the building, Xiao Ming first measured the shadow length BA of the building on the ground as 15.0 (as shown in the figure), and then set up a benchmark with a height of 2.0 at A, and measured the shadow length AC of the benchmark as 3.0, then the height of the building is ()
Choices:
A:10米
B:12米
C:15米
D:22.5米 | A |
|
As shown in the figure: the length of two vertical telephone poles AB is 6.0, the length of CD is 3.0, AD intersects BC at point E, then the length of the distance from E to the ground EF is ()
Choices:
A:2
B:2.2
C:2.4
D:2.5 | A |
|
As shown in the figure, a square DEFG model should be cut on a piece of triangle ABC paper. Among them, G and F are on BC, D and E are on AB and AC respectively, AH perpendicular BC and it intersects DE at M, if BC = 12.0, AH = 8.0, then the edge length of the square DEFG is ()
Choices:
A:\frac{24}{5}cm
B:4cm
C:\frac{24}{7}cm
D:5cm | A |
|
On 27.0 2009.0, 10.0, 2009, Shanghai team player Wu Di came to the fore in the National Games and defeated the top-seeded men's singles player Zeng Shaoxuan with a score of 2.0:0.0, and won the men's singles championship in tennis at the National Games. The picture below is a ball played by Wu Di in the final. It is known that the net height is 0.8, and the horizontal distance from the hitting point to the net is 4.0. When the ball is played, the ball can hit the net and the landing point is exactly 6.0 away from the net. Then the height h of the racket hit is ()
Choices:
A:\frac{8}{5}米
B:\frac{4}{3}米
C:1米
D:\frac{8}{15}米 | D |
|
As shown in the figure, points A, B, and C are on circle O, angle ABO = 40.0, angle ACO = 30.0, then the degree of angle BOC is ()
Choices:
A:60°
B:70°
C:120°
D:140° | B |
|
As shown in the figure, AB is a ladder leaning against the wall, the foot of the ladder is away from the wall 2.0, the point D on the ladder is away from the wall 1.8, the length of BD is 0.6, then the length of the ladder is ()
Choices:
A:5.60米
B:6.00米
C:6.10米
D:6.20米 | B |
|
In order to measure the height of the school flagpole AC, a school math interest group erected a benchmark DF with a length of 1.5 at point F. As shown in the figure, the length of the shadow EF of DF is measured as 1.0, and then measure the length of the shadow BC of the flagpole AC to be 6.0, then the height of the flagpole AC is ()
Choices:
A:6米
B:7米
C:8.5米
D:9米 | D |
|
As shown in the figure, Xiaodong uses a bamboo pole with a length of 3.2 as a measuring tool to measure the height of the school flagpole, and moves the bamboo pole so that the shadow on the top of the pole and the flag pole falls on the same point on the ground. At this time, the distance between the bamboo pole and this point is 8.0, and the distance from the flag pole is 22.0, then the height of the flag pole is ()
Choices:
A:12m
B:10m
C:8m
D:7m | A |
|
As shown in the figure, CD is a plane mirror, the light is emitted from point A, reflected by point E on CD, and irradiated to point B. If the incident angle is α, AC perpendicular CD, BD perpendicular CD, the feet of perpendicular are C, D, and AC = 3.0, BD = 6.0, CD = 10.0, then the length of the line segment ED is ()
Choices:
A:\frac{20}{3}
B:\frac{10}{3}
C:7
D:\frac{14}{3} | A |
|
As shown in the figure, Xiaoming designed two right angles to measure the width of the river BC, he measured AB = 2.0, BD = frac {7.0}{3.0}, CE = 9.0, then the width of the river BC is ()
Choices:
A:\frac{7}{2}米
B:\frac{17}{2}米
C:\frac{40}{7}米
D:11米 | C |
|
As shown in the figure, a student saw a tree by the lake. He visually observed that the distance between himself and the tree is 20.0, and the reflection of the top of the tree in the water is 5.0 far away from him. The student's height is 1.7, and the height of the tree is ( ).
Choices:
A:3.4
B:5.1
C:6.8
D:8.5 | B |
|
As shown in the figure, AB is a fixed climbing ladder leaning on the wall, the distance from the foot of the ladder B to the foot of the wall C is 1.6, the distance from the point D on the ladder to the wall is 1.4, and the length of the ladder is 0.5, then the length of the ladder is ()
Choices:
A:3.5m
B:4m
C:4.5m
D:5m | B |
|
As shown in the figure, the sunlight enters the room from the windows of the classroom, the length of the shadow of the window frame AB on the ground DE = 1.8, the distance from the lower eaves of the window to the ground BC = 1.0, EC = 1.2, then the height of the window AB is ()
Choices:
A:1.5m
B:1.6m
C:1.86m
D:2.16m | A |
|
As shown in the figure, AB is a long ladder leaning on the wall, the foot of the ladder B is away from the wall 1.6, the point D on the ladder is away from the wall 1.4, the length of BD is 0.55, then the length of the ladder is ()
Choices:
A:3.85米
B:4.00米
C:4.40米
D:4.50米 | C |
|
As shown in the figure, the student Xiao Li whose height is 1.6 wants to measure the height of the school's flagpole. When he stands at C, the shadow of the top of his head coincides with the shadow of the top of the flagpole, and AC = 2.0, BC = 8.0, then the height of the flagpole is ()
Choices:
A:6.4米
B:7米
C:8米
D:9米 | C |
|
As shown in the figure, the quadrilateral ABCD and A′B′C′D′ are similar figures with the similar center at point O. If OA′: A′A = 2.0:1.0, the area of the quadrilateral A′B′C′D′ is 12.0 ^ 2, then the area of the quadrilateral ABCD is ()
Choices:
A:24cm^{2}
B:27cm^{2}
C:36cm^{2}
D:54cm^{2} | B |
|
As shown in the figure, in triangle ABC, angle C = 90.0, if AC = 4.0, BC = 3.0, then cosB is equal to ()
Choices:
A:\frac{3}{5}
B:\frac{3}{4}
C:\frac{4}{5}
D:\frac{4}{3} | A |
|
As shown in the figure, in Rttriangle ABC, angle C = 90.0, AC = 4.0, BC = 3.0, then the value of sinB is equal to ()
Choices:
A:\frac{4}{3}
B:\frac{3}{4}
C:\frac{4}{5}
D:\frac{3}{5} | C |
|
As shown in the figure, in Rttriangle ABC, angle C = 90.0, AC = 3.0, BC = 4.0, then the value of cosA is ()
Choices:
A:\frac{3}{5}
B:\frac{5}{3}
C:\frac{4}{5}
D:\frac{3}{4} | A |
|
As shown in the figure, it is known that in Rttriangle ABC, angle C = 90.0, AB = 10.0, AC = 8.0, then the value of tanB is ()
Choices:
A:\frac{3}{5}
B:\frac{3}{4}
C:\frac{4}{5}
D:\frac{4}{3} | D |
|
As shown in the figure, the homothetic figures are composed of a triangle ruler and its center projection under the light. If the ratio of the distance from the bulb to the vertex of the triangle ruler to the distance from the bulb to the corresponding vertex of the triangular ruler projection is 2.0:5.0, and the length of one edge of the triangle ruler is 8.0, Then the corresponding edge length of the projection triangle is ()
Choices:
A:8cm
B:20cm
C:3.2cm
D:10cm | B |
|
As shown in the figure, given the angle of circumference angle BAC = 40.0, then the degree of the central angle angle BOC is ()
Choices:
A:40°
B:60°
C:80°
D:100° | C |
|
As shown in the figure, in Rttriangle ABC, angle C = 90.0, AC = 4.0, AB = 5.0, then the value of cosA is ()
Choices:
A:\frac{3}{5}
B:\frac{4}{5}
C:\frac{3}{4}
D:\frac{4}{3} | B |
|
As shown in the figure, in triangle ABC, angle C = Rtangle , AB = 5.0, AC = 4.0, then the value of sinA is ()
Choices:
A:\frac{3}{4}
B:\frac{4}{5}
C:\frac{3}{5}
D:\frac{5}{3} | C |
|
In Rttriangle ABC, angle C = 90.0, AB = 2.0, BC = 1.0, then the value of sinB is ()
Choices:
A:\frac{1}{2}
B:\frac{√{2}}{2}
C:\frac{√{3}}{2}
D:2 | C |
|
As shown in the figure, in Rttriangle ABC, it is known that angle A = 90.0, AC = 3.0, AB = 4.0, then sinB is equal to ()
Choices:
A:\frac{3}{4}
B:\frac{3}{5}
C:\frac{4}{5}
D:\frac{5}{4} | B |
|
As shown in the figure: In Rttriangle ABC, angle C = 90.0, AC = 8.0, AB = 10.0, then the value of sinB is equal to ()
Choices:
A:\frac{3}{5}
B:\frac{4}{5}
C:\frac{3}{4}
D:\frac{4}{3} | B |
|
As shown in the figure, in the plane rectangular coordinate system, the coordinates of point A are (2.0,3.0), then the value of tanα is ()
Choices:
A:\frac{2}{3}
B:\frac{3}{2}
C:\frac{2√{13}}{13}
D:\frac{3√{13}}{13} | B |
|
As shown in the figure, it is known that in Rttriangle ABC, angle C = 90.0, AC = 4.0, tanA = frac {1.0}{2.0}, then the length of BC is ()
Choices:
A:2
B:8
C:2√{5}
D:4√{5} | A |
|
As shown in the figure, in Rttriangle ABC, angle C = 90.0, AC = 4.0, AB = 5.0, then the value of sinB is ()
Choices:
A:\frac{2}{3}
B:\frac{3}{5}
C:\frac{3}{4}
D:\frac{4}{5} | D |
|
As shown in the figure, the hypotenuse of Rttriangle ABC AB = 10.0, cosA = frac {3.0}{5.0}, then the length of BC is ()
Choices:
A:5cm
B:6cm
C:3cm
D:8cm | D |
|
As shown in the figure, in the quadrilateral ABCD, E and F are the midpoints of AB and AD respectively. If EF = 2.0, BC = 5.0, CD = 3.0, then tanC is equal to ()
Choices:
A:\frac{3}{4}
B:\frac{4}{3}
C:\frac{3}{5}
D:\frac{4}{5} | B |
|
As shown in the figure, it is known that AB and AD are the chords of circle O, angle BOD = 50.0, then the degree of angle BAD is ()
Choices:
A:50°
B:40°
C:25°
D:35° | C |
|
As shown in the figure, it is known that O is a point in the quadrilateral ABCD, OA = OB = OC, angle ABC = angle ADC = 65.0, then angle DAO + angle DCO = ()
Choices:
A:90°
B:110°
C:120°
D:165° | D |
|
As shown in the figure, AC is the diameter of circle O, if angle OBC = 40.0, then the degree of angle AOB is ()
Choices:
A:40°
B:50°
C:80°
D:100° | C |
|
As shown in the figure, in circle A, the known chord BC = 8.0, DE = 6.0, angle BAC + angle EAD = 180.0, then the radius of circle A is ()
Choices:
A:10
B:6
C:5
D:8 | C |
|
As shown in the figure, the cross section of a tunnel is a semicircle with a radius of 3.4, and a truck with a width of 3.2 can pass through the tunnel.
Choices:
A:3m
B:3.4m
C:4m
D:2.8m | A |
|
As shown in the figure, triangle ABC is the inscribed triangle of circle O, if angle ACB = 30.0, AB = 6.0, then the radius of circle O is ()
Choices:
A:3
B:2√{3}
C:6
D:4√{3} | C |
|
As shown in the figure, triangle ABC is the inscribed triangle of circle O, angle C = 30.0, the radius of circle O is 5.0, if point P is a point on circle O, in triangle ABP, PB = AB, then the length of PA is ( )
Choices:
A:5
B:\frac{5√{3}}{2}
C:5√{2}
D:5√{3} | D |
|
As shown in the figure, triangle ABC is inscribed in circle O, OC perpendicular OB, OD perpendicular AB intersects AC at point E. Knowing that the radius of circle O is 1.0, then the value of AE^ 2 + CE^ 2 is ()
Choices:
A:1
B:2
C:3
D:4 | B |
|
As shown in the figure, it is known that circle O is the circumscribed circle of triangle ABC, and AB is the diameter of circle O, if OC = 5.0, AC = 6.0, then the length of BC is ()
Choices:
A:10
B:9
C:8
D:无法确定 | C |
|
As shown in the figure, angle XOY = 45.0, the two vertices A and B of a right triangle ABC move on OX and OY respectively, where AB = 10.0, then the maximum value of the distance from point O to vertex A is ()
Choices:
A:8
B:10
C:8√{2}
D:10√{2} | D |
|
As shown in the figure, it is known that the angle between the diameter AB of circle O and the chord AC is 30.0, the tangent PC passing through point C and the extended line of AB intersect at point P, the radius of circle O is 2.0, then PC is ()
Choices:
A:4
B:4√{3}
C:6
D:2√{3} | D |
|
As shown in the figure, in the circle O with a radius of 2.0, C is a point on the extended line of the diameter AB, CD is tangent to the circle at point D. Connect AD, given that angle DAC = 30.0, the length of the line segment CD is ()
Choices:
A:1
B:√{3}
C:2
D:2√{3} | D |
|
As shown in the figure, Circle O is a circle with a radius of 1.0, the distance from point O to line L is 3.0, draw a tangent of circle O through any point P on the straight line L , and the tangent point is Q; if PQ is taken as the edge to make the square PQRS, then the minimum area of the square PQRS is ()
Choices:
A:7
B:8
C:9
D:10 | B |
|
As shown in the figure, AB is the diameter of circle O, C is the point on circle O, passing point C is the tangent of circle O and intersects the extended line of AB at point E, OD perpendicular AC at point D, if angle E = 30.0, CE = 6.0, then the value of OD is ()
Choices:
A:1
B:√{3}
C:2
D:2√{3} | B |
|
As shown in the figure, the straight line AB is tangent to circle O at point A, the radius of circle O is 1.0, if angle OBA = 30.0, then the length of OB is ()
Choices:
A:1
B:2
C:√{3}
D:2√{3} | B |
|
As shown in the figure, it is known that BA is the tangent of circle O, and connect OB to intersect circle O at point C. If angle B = 45.0 and the length of AB is 2.0, then the length of BC is ()
Choices:
A:2√{2}-1
B:√{2}
C:2√{2}-2
D:2-√{2} | C |
|
As shown in the figure, point A is a point outside circle O, AB, AC, and BD are the tangents of circle O, and the tangent points are P, C, and D respectively. If AB = 5.0, AC = 3.0, then the length of BD is ()
Choices:
A:1.5
B:2
C:2.5
D:3 | B |
|
As shown in the figure, PA and PB are tangents of circle O, the tangent point of point A and B, AC is the diameter of circle O, given that angle P = 50.0, then the size of angle ACB is ()
Choices:
A:65°
B:60°
C:55°
D:50° | A |
|
As shown in the figure, points A, B, and C are on circle O, and the tangent line of circle O passing through point A intersects the extended line of OC at point P, angle B = 30.0, OP = 3.0, then the length of AP is ()
Choices:
A:3
B:\frac{3}{2}
C:\frac{2}{3}√{3}
D:\frac{3}{2}√{3} | D |
|
As shown in the figure, point P is outside circle O. PA and PB are connected. the straight lines PA and PB are the two tangents of circle O. If angle APB = 120.0, the radius of circle O is 10.0, then the length of chord AB is ()
Choices:
A:5
B:10
C:10√{3}
D:5√{3} | B |
|
As shown in the figure, PA and PB are tangent to circle O at points A and B respectively, the tangent EF of circle O intersects PA and PB at points E and F respectively, and the tangent point C is on the arc AB. If the length of PA is 2.0, then the perimeter of triangle PEF is ()
Choices:
A:8
B:6
C:4
D:2 | C |
|
Put the ruler, the triangle ruler and the round nut on the desktop as shown in the figure, angle CAB = 60.0, if AD = 6.0, then the outer diameter of the round nut is ()
Choices:
A:12cm
B:24cm
C:6√{3}cm
D:12√{3}cm | D |
|
As shown in the figure, point P is a point on the extended line AB of the diameter of circle O, passing point P to draw the tangent PC of circle O, and the tangent point is C. If AO = OB = PB = 1.0, then the length of PC is ()
Choices:
A:1
B:√{3}
C:2
D:√{5} | B |
|
As shown in the figure, a torus carpet is to be laid in the lobby of a hotel. The worker only measures the length of the chord AB of the great circle that is tangent to the small circle, and then calculates the area of the torus. If the measured length of AB is 8.0, the area of the torus is ()
Choices:
A:16平方米
B:8π平方米
C:64平方米
D:16π平方米 | D |
|
As shown in the figure, circle O is the circumcircle of triangle ABC, circle O ia tangent to AB at point C, angle BCE = 60.0, DC = 6.0, DE = 4.0, then S_triangle CDE is ()
Choices:
A:6√{5}
B:6√{3}
C:6√{2}
D:6 | B |
|
There is an isosceles triangle with side length 13 and base length 10. Find the area of the figure.
Choices:
A:30
B:60
C:120
D:240 | B |
|
Circle O has a radius of 13 inches, which is the length of O C. Radius O B is perpendicular at point X to chord C D which is 24 inches long. Find O X.
Choices:
A:5
B:12
C:13
D:26 | A |
|
There is an isosceles triangle with side length 32. The base angle is 54 degrees. x is half of the base. Find x. Round to the nearest tenth.
Choices:
A:18.8
B:23.2
C:25.9
D:44.0 | A |
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