Question: As shown in the figure, in triangle ABC, it is known that angle A = 80.0, angle B = 60.0, DE parallel  BC, then the size of angle CED is ()


Question: As shown in the figure, AB parallel  CD, straight line EF intersects AB at point E, intersects CD at point F, EG bisects angle BEF, and it intersects CD at point G, angle 1 = 50.0, then angle 2 is equal to ()


Question: As shown in the figure, BD bisects angle ABC, CD parallel  AB, if angle BCD = 70.0, then the degree of angle CDB is ()


Question: As shown in the figure, AB ia tangent to circle O at point B, and the extended line of AO intersects circle O at point C. Connect BC, if angle A = 36.0, then angle C is equal to ()


Question: As shown in the figure, straight lines a and b intersect at point O. If angle 1 is equal to 50.0, then angle 2 is equal to ()


Question: As shown in the figure, AB // CD, and EF intersects AB and CD at points E, F, angle 1 = 50.0, then the degree of angle 2 is ()


Question: As shown in the figure, triangle ABC congruent  triangle ADE, if angle B = 70.0, angle C = 30.0, angle DAC = 35.0, then the degree of angle EAC is ()


Question: As shown in the figure, triangle ABC congruent  triangle DEF, points A and D, B and E are the corresponding vertices, and the measured BC = 5.0, BF = 7.0, then the length of EC is ()


Question: As shown in the figure, in triangle ABC, angle C = 90.0, AC = BC, AD bisects angle CAB and it intersects BC at D, DE perpendicular  AB at E, if AB = 6.0, then the perimeter of triangle DBE is ()


Question: As shown in the figure, in triangle ABC, AB = AC, angle A = 36.0, the perpendicular bisector of AB intersects AC at D, and intersects AB at E, then the degree of angle BDC is ()


Question: As shown in the figure, in triangle ABC, angle C = 36.0, rotate triangle ABC anticlockwise around point A by 60.0 to get triangle AED, AD and BC intersect at point F, then the degree of angle AFC is ()


Question: As shown in the figure, the straight line AB parallel  CD, Rttriangle DEF is placed as shown, angle EDF = 90.0, if angle 1 + angle F = 70.0, then the degree of angle 2 is ()


Question: As shown in the figure, AB parallel  EF, CD perpendicular  EF, angle BAC = 50.0, then angle ACD = ()


Question: As shown in the figure, triangle ABC is the inscribed triangle of circle O, angle OAB = 35.0, then the degree of angle ACB is ()


Question: Place the ruler and the right triangle board as shown in the figure (angle ACB is a right angle), it is known that angle 1 = 30.0, then the size of angle 2 is ()


Question: As shown in the figure, the straight line a and the straight line b are intercepted by the straight line c, b perpendicular  c, the foot of perpendicular is the point A, angle 1 = 70.0. If the line b is parallel to the line a, the line b can be rotated () clockwise around the point A


Question: As shown in the figure, in circle O, chord AC parallel  radius OB, angle BOC = 50.0, then the degree of angle OAB is ()


Question: In □ABCD, the diagonal AC and BD intersect at point O, angle DAC = 42.0, angle CBD = 23.0, then angle COD is ().


Question: The positions of straight lines a, b, c, and d are shown in the figure. If angle 1 = 58.0, angle 2 = 58.0, angle 3 = 70.0, then angle 4 is equal to ()


Question: As shown in the figure, a parallel  b, angle 1 = 158.0, angle 2 = 42.0, angle 4 = 50.0. Then angle 3 = ()


Question: As shown in the figure, AB is the diameter of circle O, C and D are two points on circle O. Connect AC, BC, CD, and OD respectively. If angle DOB = 140.0, then angle ACD = ()


Question: As shown in the figure, it is known that angle 1 = angle 2 = angle 3 = 55.0, then the degree of angle 4 is ()


Question: As shown in the figure, in the diamond ABCD, M and N are respectively AB and CD, and AM = CN, MN and AC intersect at point O. Connect BO. If angle DAC = 28.0, then the degree of angle OBC is ()


Question: As shown in the figure, PA and PB are tangent to circle O at A and B respectively. If angle C = 65.0, then the degree of angle P is ()


Question: As shown in the figure, the line a parallel  b and they intersect the line c at a and b respectively, angle 1 = 50.0, then the degree of angle 2 is ()


Question: As shown in the figure, EF parallel  BC, AC bisects angle BAF, angle B = 50.0, then the degree of angle C is ()


Question: As shown in the figure, in order to measure the height of the school flagpole, Xiaodong uses a bamboo pole with a length of 3.2 as a measuring tool, and moves the bamboo pole so that the top of the bamboo pole and the shadow of the top of the flag pole fall on the same point on the ground. At this time, the distance between the bamboo pole and this point is 8.0 , 22.0 from the flagpole, the height of the flagpole is ().


Question: As shown in the figure, when planting trees on flat ground, the plant spacing (the horizontal distance between two adjacent trees) is required to be 4.0. If trees are planted on a hillside with a slope of 0.75, and the plant spacing is also required to be 4.0, then the slope distance between two adjacent trees is ()


Question: As shown in the figure, the right triangle ABC and the equilateral triangle ABD are respectively drawn with the line segment AB as the edge, where angle ACB = 90.0. Connect CD, when the length of CD is the largest, the size of angle CAB is ()


Question: As shown in the figure, D is the intersection point of the angular bisector BD and CD of triangle ABC. If angle A = 50.0, then angle D = ()


Question: As shown in the figure, it is known that OA = OB = OC and angle ACB = 30.0, then the size of angle AOB is ()


Question: As shown in the figure, the straight line a parallel  b, the point B is on the straight line b, and AB perpendicular  BC, angle 2 = 65.0, then the degree of angle 1 is ()


Question: Circle I is the inscribed circle of triangle ABC, D, E, F are 3.0 tangent points, if angle DEF = 52.0, then the degree of angle A is ()


Question: As shown in the figure, the straight line AB parallel  CD, angle 1 = 136.0, angle E is a right angle, then angle C is equal to ()


Question: As shown in the figure, the straight lines AB and CD are intercepted by the straight line EF. If AB parallel  CD, angle 1 = 100.0, then the size of angle 2 is ()


Question: As shown in the figure: AB parallel  DE, angle B = 30.0, angle C = 110.0, the degree of angle D is ()


Question: As shown in the figure, AB is the diameter of circle O, point C is on circle O, passing point C to draw the tangent of circle O and it intersects the extended line of AB at point D. Connect AC. If angle D = 50.0, then the degree of angle A is ()


Question: As shown in the figure, AB parallel  CD, CP intersects AB at O, AO = PO, if angle C = 50.0, then the degree of angle A is ()


Question: As shown in the figure, in triangle ABC, AB = AC, passing point A to draw AD parallel  BC. If angle 1 = 70.0, then the size of angle BAC is ()


Question: Fold a rectangular piece of paper with equal width as shown in the figure. If angle 1 = 140.0, then the degree of angle 2 is ()


Question: As shown in the figure, it is known that the straight lines a and b are intercepted by the straight line c, a parallel  b, angle 1 = 50.0, then angle 2 = ()


Question: The positions of straight lines a, b, c, and d are shown in the figure. If angle 1 = 100.0, angle 2 = 100.0, angle 3 = 125.0, then angle 4 is equal to ()


Question: The figure is a schematic diagram of a kite stand made by Xiao Liu. It is known that BC parallel  PQ, AB: AP = 2.0:5.0, AQ = 20.0, then the length of CQ is ()


Question: As shown in the figure, triangle ODC is the figure obtained by rotating triangle OAB clockwise around point O by 30.0. If point D happens to fall on AB, and the degree of angle AOC is 100.0, then the degree of angle DOB is ()


Question: As shown in the figure, the two street lamps A and B are separated by 30.0. One night, when Xiaogang went straight 25.0 from the bottom of street lamp A to the bottom of street lamp B, he found that the top of his figure just touched the bottom of street lamp B. It is known that Xiaogang's height is 1.5, then the height of the street lamp is ()


Question: As shown in the figure, C is a point on circle O, O is the center of the circle, if angle C = 35.0, then the degree of angle AOB is ()


Question: As shown in the figure, if AB parallel  CD, angle A = 70.0, then the degree of angle 1 is ()


Question: As shown in the figure, the straight line AB parallel  CD, angle C = 44.0, angle E is a right angle, then angle 1 is equal to ()


Question: As shown in the figure, A, B, C are any three points on circle O, if angle BOC = 100.0, then the degree of angle BAC is ()


Question: As shown in the figure, in the inscribed pentagon ABCDE of circle O, angle CAD = 35.0, angle AED = 115.0, then the degree of angle B is ()


Question: As shown in the figure, in triangle ABC, angle C = 90.0, AD is the bisector of angle BAC, DE perpendicular  AB at E, if DE = 8.0, DB = 10.0, then BC is equal to ()


Question: As shown in the figure, the straight lines AB and CD intersect at point O, EO perpendicular  AB, and the foot of perpendicular is point O, angle BOD = 50.0, then angle COE = ()


Question: As shown in the figure, the points B, E, C, and F are on the same straight line, triangle ABC congruent  triangle DEF, angle B = 45.0, angle F = 65.0, then the degree of angle COE is ()


Question: As shown in the figure, put the two vertices of a right triangle plate with 45.0 angles on the opposite edges of the ruler. If angle 1 = 27.5, then angle 2 is equal to ()


Question: As shown in the figure, the straight line a parallel  b, the point B is on the straight line b, and AB perpendicular  BC, angle 1 = 55.0, then the degree of angle 2 is ()


Question: As shown in the figure, the straight line a parallel  b, the straight line c intersects a and b, angle 1 = 55.0, then angle 2 = ()


Question: Place a ruler and a triangular plate as shown in the figure, angle 1 = 40.0, then the degree of angle 2 is ()


Question: As shown in the figure, the straight lines AB and CD intersect at point O, and the radial OM bisects angle AOC, ON perpendicular  OM. If angle AOC = 70.0, then the degree of angle CON is ()


Question: As shown in the figure, the diameter CD of circle O crosses the midpoint G of chord EF, angle DCF = 20.0, then angle EOD is equal to ()


Question: As shown in the figure, AB is parallel to CD, if angle B = 20.0, then angle C is ()


Question: As shown in the figure, AB parallel  CD, angle CED = 90.0, angle AEC = 35.0, then the size of angle D is ()


Question: As shown in the figure, AB parallel  CD, AD bisects angle BAC, and angle C = 80.0, then the degree of angle D is ()


Question: As shown in the figure, AB parallel  CD, if angle 2 = 135.0, then the degree of angle 1 is ()


Question: As shown in the figure, AB parallel  CD, point E is on BC, and CD = CE, angle D = 74.0, then the degree of angle B is ()


Question: As shown in the figure, AB parallel  CD, point E is on the extended line of CA. If angle BAE = 40.0, then the size of angle ACD is ()


Question: As shown in the figure, use the benchmark BE to measure the height of the tree CD. If the length of the benchmark BE is 2.0, AB = 3.0, AC = 9.0, and the points A, E, and D are on a straight line, then the tree CD is ()


Question: After filling some oil in a cylindrical oil tank with a diameter of 200.0, the cross section is shown in the figure. If the width of the oil surface AB = 160.0, the maximum depth of oil is ()


Question: As shown in the figure, angle 1 = angle 2, angle 3 = 30.0, then angle 4 is equal to ()


Question: As shown in the figure, AB parallel  CD, angle B = 20.0, angle D = 60.0, then the degree of angle BED is ()


Question: As shown in the figure, the straight line AB parallel  CD, AE bisects angle CAB, angle ACD = 40.0, then the degree of angle AEC is ()


Question: Xuan Xuan and Kai Kai are in the same mathematics study group. In a math activity class, they each used a square piece of paper with a side length of 12.0 to make a pair of jigsaw puzzles, and cooperated to design the work shown in the picture. Help them calculate the sum of the area of the three figures circled in the figure, it is ()


Question: As shown in the figure, the straight line a parallel  b, angle 2 = 35.0, angle 3 = 40.0, then the degree of angle 1 is ()


Question: As shown in the figure, BD is the angular bisector of triangle ABC, AE perpendicular  BD, and the foot of perpendicular is F. If angle ABC = 35.0, angle C = 50.0, then the degree of angle CDE is ()


Question: As shown in the figure, the straight line AD parallel  BC, if angle 1 = 42.0, angle BAC = 78.0, then the degree of angle 2 is ()


Question: As shown in the figure, the perimeter of □ABCD is 16.0, AC and BD intersect at point O, and OE perpendicular  AC and it intersects AD at point E, then the perimeter of triangle DCE is ()


Question: As shown in the figure, triangle ABC is the inscribed triangle of circle O. If angle ABC = 70.0, then the degree of angle AOC is equal to ()


Question: As shown in the figure, AB parallel  CD, radial AE intersects CD at point F, if angle 1 = 115.0, then the degree of angle 2 is ()


Question: As shown in the figure, a // b, put the right-angled vertex of a triangular plate on the straight line a, angle 1 = 42.0, then the degree of angle 2 is ()


Question: As shown in the figure, a parallel  b, point B is on the straight line b, and AB perpendicular  BC, angle 1 = 36.0, then angle 2 = ()


Question: As shown in the figure, if angle 1 = angle 3, angle 2 = 60.0, then the degree of angle 4 is ()


Question: As shown in the figure, AB parallel  CD, AE bisects angle CAB and CD at point E, if angle C = 70.0, then the degree of angle AED is ()


Question: As shown in the figure, the perimeter of parallelogram ABCD is 32.0, AC, BD intersect at point O, and OE perpendicular  AC and it intersects AD at point E, then the perimeter of triangle DCE is ()


Question: As shown in the figure, a cylinder with a bottom circumference of 24.0 and a height of 5.0, the shortest route that an ant passes along the surface from point A to point B is ()


Question: As shown in the figure, in triangle ABC, angle BAC = 90.0, AD perpendicular  BC at point D, AE bisects angle DAC, angle B = 50.0, so the degree of angle DAE is ()


Question: As shown in the figure, the line l parallel  m parallel  n, the vertices B and C of the triangle ABC are on the line n and line m, the angle between BC and the line n is 25.0, and angle ACB = 60.0, then the degree of angle a is ()


Question: As shown in the figure, it is known that in circle O, the central angle angle AOB = 100.0, then the angle of circumference angle ACB is equal to ().


Question: As shown in the figure, triangle ABC is inscribed in circle O with radius 1.0, if angle BAC = 60.0, then the length of BC is ()


Question: As shown in the figure, the circle O is the circumscribed circle of triangle ABC, and the bisector of angle BAC and angle ABC intersects at point I. Extend AI and it intersects circle O at point D. Connect BD and DC. If the radius of circle O is 8.0, angle BAC = 120.0, then the length of DI is ()


Question: As shown in the figure, circle O is the circumscribed circle of triangle ABC. Connect OB and OC, if the radius of circle O is 2.0, angle BAC = 60.0, then the length of BC is ()


Question: As shown in the figure, AB and CD are the two diameters of circle O, chord DE parallel  AB, arc DE is the arc of 50.0, then angle BOC is ()


Question: As shown in the figure, points A, B, and C are on circle O, angle ABO = 22.0, angle ACO = 42.0, then angle BOC is equal to ()


Question: As shown in the figure, A, B, C are three points on circle O, angle ACB = 25.0, then the degree of angle BAO is ()


Question: As shown in the figure, it is known that in circle O, angle AOB = 50.0, then the degree of the angle of circumference angle ACB is ()


Question: As shown in the figure, AB is the diameter of circle O, C and D are two points on circle O, angle BAC = 30.0, arc AD = arc CD. Then angle DAC is equal to ()


Question: As shown in the figure, AB is the diameter of circle O, C and D are two points on the circle, angle D = 34.0, then the degree of angle BOC is ()


Question: As shown in the figure, points A, B, and C are all on circle O, when angle OBC = 40.0, the degree of angle A is ()


Question: As shown in the figure, the diameter AB of circle O is perpendicular to the chord CD, the foot of perpendicular is the point E, angle CAO = 22.5, OC = 6.0, then the length of CD is ()


Question: As shown in the figure, in circle O, chord BC and radius OA intersect at point D. Connect AB and OC. If angle A = 60.0, angle ADC = 90.0, then the degree of angle C is ()


Question: As shown in the figure, points A, B, and P are three points on circle O, if angle AOB = 40.0, then the degree of angle APB is ()


Question: As shown in the figure, AB is the chord of circle O, OC perpendicular  AB and it intersects circle O at point C. Connect OA, OB, BC, if angle ABC = 25.0, then the size of angle AOB is ()


Question: As shown in the figure, given the angle of circumference angle A = 50.0, then the size of angle OBC is ()


Question: As shown in the figure, AB is the diameter of circle O, CD is the chord of circle O, angle ADC = 26.0, then the degree of angle CAB is ()


Question: As shown in the figure, in circle O, AB is the diameter, CD is the chord, AB perpendicular  CD, the foot of perpendicular is the point E. Connect CO and AD, if angle BOC = 30.0, then the degree of angle BAD is ()


Question: 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 = ()


Question: 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 ()


Question: 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 = ()


Question: 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 ()


Question: 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 ()


Question: 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 ()


Question: 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 ()


Question: 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 ()


Question: As shown in the figure, it is known that angle α = 130.0, then angle β = ()


Question: 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 ()


Question: 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 ()


Question: 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 ()


Question: 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 = ()


Question: 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 ()


Question: 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 ()


Question: 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) ()


Question: 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 ()


Question: 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 ()


Question: 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 ()


Question: 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 ()


Question: 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) ()


Question: 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 ()


Question: 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 ()


Question: 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 ()


Question: 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 ()


Question: 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 ()


Question: 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 ()


Question: 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 ()


Question: 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 ()


Question: 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 ()


Question: 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 ()


Question: 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 ()


Question: 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 ()


Question: 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 ()


Question: 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 ()


Question: 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 ()


Question: 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 ()


Question: 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 ().


Question: 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 ()


Question: 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 = ()


Question: 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 ()


Question: 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 ()


Question: 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 ()


Question: 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 ()


Question: 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 ()


Question: 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 ()


Question: 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 ()


Question: 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 ()


Question: 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 ()


Question: 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 ()


Question: 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 ( ).


Question: 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 ()


Question: 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 ()


Question: 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 ()


Question: 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 ()


Question: 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 ()


Question: As shown in the figure, in triangle ABC, angle C = 90.0, if AC = 4.0, BC = 3.0, then cosB is equal to ()


Question: 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 ()


Question: As shown in the figure, in Rttriangle ABC, angle C = 90.0, AC = 3.0, BC = 4.0, then the value of cosA is ()


Question: 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 ()


Question: 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 ()


Question: As shown in the figure, given the angle of circumference angle BAC = 40.0, then the degree of the central angle angle BOC is ()


Question: As shown in the figure, in Rttriangle ABC, angle C = 90.0, AC = 4.0, AB = 5.0, then the value of cosA is ()


Question: As shown in the figure, in triangle ABC, angle C = Rtangle , AB = 5.0, AC = 4.0, then the value of sinA is ()


Question: In Rttriangle ABC, angle C = 90.0, AB = 2.0, BC = 1.0, then the value of sinB is ()


Question: 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 ()


Question: In Rttriangle ACB, angle C = 90.0, BC = 5.0, AC = 12.0, then sinA = ()


Question: As shown in the figure, in the rectangular coordinate system, P is the point in the first quadrant, and its coordinates are (4.0,m), and the cosine value of the angle α between OP and the positive semi-axis of the x-axis is frac {3.0}{5.0}, then the value of tanangle α is ()


Question: As shown in the figure, it is known that in Rttriangle ABC, angle C = 90.0, AC = 6.0, BC = 8.0, then the value of tanA is ()


Question: 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 ()


Question: As shown in the figure, in Rttriangle ABC, angle C = 90.0, AC = 1.0, BC = 2.0, then the value of cosB is ()


Question: 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 ()


Question: 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 ()


Question: As shown in the figure, in ABC, AB = AC = 4.0, BC = 6.0, then cosB = ()


Question: As shown in the figure, in Rttriangle ABC, angle C = 90.0, AC = 4.0, AB = 5.0, then the value of sinB is ()


Question: As shown in the figure, the four small squares with edge length of 1.0 form a large square. A, B, and O are the vertices of the small squares, the radius of circle O is 1.0, and P is the point on circle O, and the small square is located at the upper right. , then sinangle APB is equal to ()


Question: 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 ()


Question: 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 ()


Question: In Rttriangle ABC, angle ACB = 90.0, CD perpendicular  AB at point D, if AC = 3.0, BC = 4.0, then tanα is equal to ()


Question: As shown in the figure, in Rttriangle ABC, angle C = 90.0, sinA = frac {1.0}{3.0}, then the value of cosB is ()


Question: We know that if the sum of two acute angles is equal to a right angle, then these two angles are complementary to each other, referred to as complementary to each other. As shown in the figure, angle A and angle B are complementary, and there are: sinA = frac  angle A's opposite hypotenuse = frac  ac, \cosB = frac  angle B's adjacent hypotenuse = frac  ac, so we know sinA = \cosB, notice that in triangle ABC, angle A + angle B = 90.0, that is, angle B = 90.0-angle A, angle A = 90.0-angle B, so there is: sin( 90.0-A) = \cosA, \ cos( 90.0-A) = sinA. Try to complete the following multiple-choice questions: If α is an acute angle and \cosα = frac {4.0}{5.0}, then the value of sin(90.0-α) is equal to ()


Question: 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 ()


Question: As shown in the figure, in triangle ABC, the bisectors of the exterior angles of angle ABC and angle ACB intersects at point O, and angle BOC = 40.0, then angle A = ()


Question: As shown in the figure, it is known that CD is the diameter of circle O, and the chord DE passing through the point D is parallel to the radius OA. If the angle D = 50.0, the degree of the angle C is ()


Question: As shown in the figure, point B is on circle O, chord AC parallel  OB, angle BOC = 50.0, then angle OAB = ()


Question: As shown in the figure, points A, B, and C are three points on circle O, if angle A = 40.0, then the degree of angle BOC is ()


Question: In circle O, AB is the diameter, CD is the chord, angle ABD = 28.0, then the degree of angle C is ()


Question: As shown in the figure, points A, B, and C are three points on circle O, if angle BOC = 80.0, then the degree of angle A is ()


Question: As shown in the figure, AB is the diameter of circle O, CD is the chord of circle O, angle CDB = 40.0, then the degree of angle CBA is ()


Question: 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 = ()


Question: As shown in the figure, AB is the diameter of circle O, angle D = 33.0, then the degree of angle AOC is ()


Question: As shown in the figure, in circle O, OA perpendicular  BC, angle AOB = 48.0, D is a point on circle O, then the degree of angle ADC is ()


Question: As shown in the figure, the three points A, B, and C are on circle O, angle ABO = 50.0, then angle ACB = ()


Question: As shown in the figure, AC is the diameter of circle O, if angle OBC = 40.0, then the degree of angle AOB is ()


Question: 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 ()


Question: Place the protractor on a broken piece of glass as shown in the figure, so that point A is on a semicircle, and the readings of points B and C are 105.0 and 155.0 respectively, then the size of angle BAC is ()


Question: As shown in the figure, points A and B are three points on circle O and AB = AC. Connect BO and CO, if angle ABC = 65.0, then the degree of angle BOC is ()


Question: As shown in the figure, given that the degree of the central angle angle AOB is 110.0, then the angle of circumference angle ACB is equal to ()


Question: 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.


Question: As shown in the figure, AB and CD are the two diameters of circle O, the chord DE parallel  AB, if the arc DE is the arc of 40.0, then angle BOC = ()


Question: As shown in the figure, in circle O, if point C is the midpoint of arc AB, angle A = 50.0, then angle BOC = ()


Question: If AB parallel  CD, angle C = 60.0, then angle A + angle E is equal to ()


Question: Known: As shown in the figure, in circle O, OA perpendicular  BC, angle AOB = 70.0, then the degree of angle ADC is ()


Question: As shown in the figure, CD is the chord of circle O, O is the center of the circle, fold the minor arc of circle O in half along CD, A is a point on the minor arc after folding in half, angle CAD = 110.0, then the degree of angle B is ()


Question: As shown in the figure, AB is the diameter of circle O, point C is a point on circle O, angle C = 20.0, then the degree of angle BOC is ()


Question: As shown in the figure, circle O is the circumscribed circle of triangle ABC, if angle AOB = 130.0, then the degree of angle ACB is ()


Question: As shown in the figure, in circle O, chord AB and CD intersect at point E, BE = DE, angle B = 40.0, then the degree of angle A is ()


Question: As shown in the figure, points A, B, C, D are on circle O, DE perpendicular  OA, DF perpendicular  OB, and the feet of perpendicular are E, F respectively. If angle EDF = 50.0, then the degree of angle C is ()


Question: As shown in the figure, CD is the diameter of circle O, chord AB intersects CD at point M, M is the midpoint of AB, point P is at arc AD, PC and AB intersect at point N, angle PNA = 60.0, then angle PDC is equal to ( )


Question: As shown in the figure, AB is the diameter of circle O, chord CD perpendicular  AB at E. Connect OC and AD, and angle A = 35.0, then angle AOC = ()


Question: As shown in the figure, in triangle ABC, AB = AC, draw a semicircle with BC as the diameter to intersect AB at E, and it intersects AC at D, the degree of arc CD is 40.0, then the degree of angle A is ()


Question: As shown in the figure, the points A, B, C, and P are on circle O, CD perpendicular  OA, CE perpendicular  OB, and the feet of perpendicular are D, E, angle DCE = 36.0, then the degree of angle P is ()


Question: As shown in the figure, points A, B, C, and P are on circle O, CD perpendicular  OA, CE perpendicular  OB, and the feet of perpendicular are D, E, angle DCE = 40.0, then the degree of angle P is ()


Question: As shown in the figure, the three points A, B, and C are on the circle. In triangle ABC, angle ABC = 70.0, angle ACB = 30.0, D is the midpoint of the arc BAC. Connect DB and DC, then the degree of angle DBC is ()


Question: As shown in the figure, AB and CD are the two chords of circle O. Connect AD and BC, if angle BCD = 50.0, then the degree of angle BAD is ()


Question: As shown in the figure, triangle ABC is inscribed in circle O, if angle OAB = 26.0, then the size of angle C is ()


Question: As shown in the figure, circle O is the circumscribed circle of triangle ABC, angle A = 70.0, then the size of angle BOC is ()


Question: As shown in the figure, in circle O, chord AC parallel  radius OB, angle BOC = 50.0, then the degree of angle OBA is ()


Question: As shown in the figure, if angle ABC = 30.0, then the degree of angle AOC is ()


Question: As shown in the figure, in circle O, CD is the diameter, point A, point B on circle O, connect OA, OB, AC, AB, if angle AOB = 40.0, CD parallel  AB, then the size of angle BAC is ()


Question: As shown in the figure, it is a circular exhibition hall. In order to monitor the entire exhibition hall, two monitors A and B are installed on the circular edge. If the monitoring angle of monitor A is 65.0, the monitoring angle of monitor B is at least ( )


Question: As shown in the figure, circle O is the circumscribed circle of triangle ABC. Connect OA and OB, angle AOB = 50.0, then the degree of angle C is ()


Question: It is known that: as shown in the figure, AB is the diameter of circle O, CD is the chord,. Connect AD, AC, angle CAB = 55.0, then angle D = ()


Question: As shown in the figure, points A, B, and C are on circle O, if angle C = 35.0, then angle AOB = ()


Question: As shown in the figure, AB is the diameter of circle O, and the degree of angle ADC is 35.0, then the degree of angle BOC is ()


Question: As shown in the figure, the quadrilateral ABCD is inscribed in circle O, AB is the diameter of circle O, and point C is the midpoint of arc BD. If angle DAB = 50.0, then the size of angle ABC is ()


Question: As shown in the figure, the quadrilateral ABCD is the inscribed quadrilateral of circle O, AB is the diameter of circle O. Connect BD. If angle BCD = 120.0, then the size of angle ABD is ()


Question: As shown in the figure, points A, B, C, and D are on circle O, and point E is on the extended line of AD. If angle ABC = 60.0, then the degree of angle CDE is ()


Question: As shown in the figure, the quadrilateral ABCD is inscribed in the semicircle O, and it is known that angle ADC = 140.0, then the size of angle AOC is ()


Question: As shown in the figure, the quadrilateral ABCD is inscribed in circle O. If angle BOD = 138.0, then the degree of one of its exterior angles angle DCE is ()


Question: As shown in the figure, the quadrilateral ABCD is inscribed in circle O, E is a point on the BC extended line, angle A = 50.0, then the degree of angle DCE is ()


Question: As shown in the figure, the quadrilateral ABCD is inscribed in circle O, F is a point on arc CD, and arc DF = arc BC, connect CF and extend to intersects the extended line of AD at point E, connect AC. If angle ABC = 105.0, angle BAC = 25.0, then the degree of angle E is ()


Question: As shown in the figure, the quadrilateral ABCD is the inscribed quadrilateral of circle O, if angle C = 140.0, then the degree of angle BOD is ()


Question: As shown in the figure, in circle O, AB parallel  CD, angle BCD = 100.0, E is any point on arc DC, A, B, C, and D are the four points on circle O, then the angle of angle AEC is ()


Question: As shown in the figure. Given that the three points A, B, and C are on circle O, point C is on the minor arc AB, and angle AOB = 130.0, then the degree of angle ACB is ()


Question: As shown in the figure, the quadrilateral ABCD is inscribed in circle O, if angle ABC = 40.0, then the degree of angle ADC is ()


Question: As shown in the figure, an exterior angle of the quadrilateral ABCD angle DCE = 70.0, then the degree of angle BAD is ()


Question: As shown in the figure, the quadrilateral ABCD is inscribed in circle O, angle BOD = 70.0, then the degree of angle BCD is ()


Question: As shown in the figure, the quadrilateral ABCD is inscribed in circle O, if one of its exterior angles angle DCE = 64.0, then angle BOD = ()


Question: As shown in the figure, the quadrilateral ABCD is a quadrilateral inscribed in the circle, and E is a point on the extended line of AD. If angle CBA = 120.0, then the size of angle EDC is ()


Question: As shown in the figure, in the circle inscribed in the quadrilateral ABCD, the central angle angle 1 = 100.0, then the angle of circumference angle ABC is equal to ()


Question: As shown in the figure, in the inscribed quadrilateral ABCD of the circle, angle ABC = 120.0, then the degree of the exterior angle of the quadrilateral ABCD angle ADE is ()


Question: As shown in the figure, ABCD is the inscribed quadrilateral of circle O, and angle ABC = 115.0, then angle AOC is equal to ()


Question: As shown in the figure, given the angle of circumference angle BAD = 50.0, then the degree of the angle of circumference angle BCD is ()


Question: As shown in the figure, circle O is the circumscribed circle of the quadrilateral ABCD, if angle O = 110.0, then the degree of angle C is ()


Question: As shown in the figure, the quadrilateral ABCD is inscribed in circle O, if angle C = 36.0, then the degree of angle A is ()


Question: As shown in the figure, there are four points A, B, C, D on circle O, where angle A = 80.0, then the degree of angle C is ()


Question: 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 ()


Question: As shown in the figure, the line segment AB is the diameter of circle O, the chord CD 丄 AB, angle CAB = 20.0, then angle BOD is equal to ()


Question: As shown in the figure, triangle ABC is the inscribed triangle of circle O, AB is the diameter of circle O, point D is a point on circle O, if angle ACD = 40.0, then the size of angle BAD is ()


Question: As shown in the figure, triangle ABC is inscribed in circle O, angle C = 20.0, then the degree of angle OAB is ()


Question: As shown in the figure, triangle ABC is inscribed in circle O. Connect OA, OB, if angle C = 35.0, then the degree of angle OBA is ()


Question: As shown in the figure, it is known that triangle ABC is inscribed in circle O, angle BAC = 50.0, then the degree of angle BOC is ()


Question: As shown in the figure, in triangle ABC, AB = AC, angle BAC = 70.0, circle O is the circumscribed circle of triangle ABC, point D is on the minor arc arc AC, then the degree of angle D is ()


Question: As shown in the figure, triangle ABC is inscribed in circle O, angle AOB = 80.0, then the size of angle ACB is ()


Question: 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 ( )


Question: 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 ()


Question: 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 ()


Question: 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 ()


Question: As shown in the figure, in triangle ABC, angle BAC = 70.0, angle ABC = 45.0, point O is the center of the circumscribed circle of triangle ABC, then angle AOB is equal to ()


Question: As shown in the figure, circle O is the circumscribed circle of triangle ABD, if angle A = 135.0, then the degree of angle BDO is ()


Question: As shown in the figure, triangle ABC is inscribed in circle O, if angle AOB = 110.0, then the degree of angle ACB is ()


Question: 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 ()


Question: As shown in the figure, AB cuts circle O at point B, AO intersects circle O at point C, and point D is at circle O. If angle A = 40.0, then the degree of angle BDC is ()


Question: As shown in the figure, AB is the diameter of circle O, point D is on the extended line of AB, passing point D is the tangent of circle O, and the tangent point is C, if angle A = 25.0, then angle D = ()


Question: 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 ()


Question: 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 ()


Question: 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 ()


Question: 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 ()


Question: 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 ()


Question: As shown in the figure, AB is the diameter of circle O, point P is a point outside circle O, PO intersects circle O at point C. Connect BC and PA. If angle P = 36.0, PA is tangent to circle O, then angle B is equal to ()


Question: As shown in the figure, 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 ()


Question: As shown in the figure, AB is the diameter of circle O, PA is tangent to circle O at point A, line segment PO intersects circle O at point C, and connect BC, if angle P = 36.0, then angle B is equal to ()


Question: 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 ()


Question: 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 ()


Question: As shown in the figure, in circle O, AD and CD are chords. Connect OC and extend, and it intersects the tangent of point A at point B. If angle ADC = 25.0, then the degree of angle ABO is ()


Question: As shown in the figure, 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 ()


Question: As shown in the figure, AC is the tangent of circle O, the tangent point is C, BC is the diameter of circle O, AB intersects circle O at point D. Connect OD, if angle BAC = 50.0, then the size of angle COD is ()


Question: As shown in the figure, AB is the diameter of circle O, BP is the tangent of circle O, AP and circle O intersect at point G, point D is the point on arc BC, if angle P = 40.0, then angle ADC is equal to ()


Question: As shown in the figure, AB is the diameter of circle O, PA is tangent to circle O at point A, OP intersects circle O at point C, and connect BC. If angle P = 20.0, then the degree of angle B is ()


Question: 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 ()


Question: 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 ()


Question: AB is the diameter of circle O, PA is tangent to circle O at point A, and PO intersects circle O at point C; connect BC, if angle P = 40.0, then angle B is equal to ()


Question: As shown in the figure, AB is the diameter of circle O, DB and DC are respectively tangent to circle O at points B and C. If angle ACE = 25.0, then the degree of angle D is ()


Question: As shown in the figure, AB is the tangent of circle O, A is the tangent point, the extended line of BO intersects circle O at point C, angle OAC = 35.0, then the degree of angle B is ()


Question: As shown in the figure, in triangle ABC, angle B = 20.0, point O is a point on the edge of BC, take O as the center and OB as the radius to make a circle, intersect the AB edge at point D, connect CD, if CD happens to be tangent of circle O , then the degree of angle DCB is ()


Question: As shown in the figure, PA and PB are the tangents of circle O, points A and B are the tangent points, and AC is the diameter of circle O. Given that angle P = 50.0, the size of angle ACB is ()


Question: As shown in the figure, PA and PB are tangent to circle O at two points A and B respectively, point C is on the major arc arc ACB, angle P = 80.0, then the degree of angle C is ()


Question: As shown in the figure, circle O is the circumscribed circle of Rttriangle ABC, angle ACB = 90.0, angle A = 25.0, crossing point C to draw the tangent of circle O, and intersects the extended line of AB at point D, then the degree of angle D is ()


Question: As shown in the figure, AB is the diameter of circle O, point C is on the extended line of AB, CD is tangent to circle O, and the tangent point is D. If angle A = 35.0, then angle C = ()


Question: 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 ()


Question: As shown in the figure, in triangle ABC, AB = 5.0, BC = 3.0, AC = 4.0, the circle with point C as the center is tangent to AB, then the radius of circle C is ()


Question: As shown in the figure, points A, B, and C are three points on circle O, and the straight line CD and circle O are tangent to point C. If angle DCB = 40.0, then the degree of angle CAB is ()


Question: As shown in the figure, the straight line AB and circle O are tangent to point A, the radius of circle O is 2.0, if angle OBA = 30.0, then the length of AB is ()


Question: As shown in the figure, AB is the diameter of circle O, AC is tangent to circle O at A, BC intersects circle O at point D, if angle C = 70.0, then the degree of angle AOD is ()


Question: As shown in the figure, PA and PB are tangent to circle O at points A and B respectively, point E is a point on circle O, and angle AEB = 60.0, then angle P = ()


Question: As shown in the figure, PA and PB are the tangents of circle O, AC is the diameter of circle O, angle c = 55.0, then angle APB is equal to ()


Question: As shown in the figure, PA and PB are tangent to circle O at A and B respectively, angle P = 70.0, then angle C is ()


Question: As shown in the figure, the line segment AB is the diameter of circle O, points C and D are points on circle O, and the tangent of circle O passing through point C intersects the extended line of AB at point E. If angle E = 50.0, then angle CDB is equal to ( )


Question: The straight line AB and circle O are tangent to point A, as shown in the figure, if angle OBA = 60.0, AB = 1.0, then the radius of circle O is ()


Question: As shown in the figure, in Rttriangle ABC, AC = 4.0, AB = 5.0, angle C = 90.0, the circle passing through point C which is tangent to the edge AB intersects the edges CB and CA of triangle ABC at points E, F. The minimum length of the line segment EF is ()


Question: As shown in the figure, the radii of the two concentric circles are 3.0 and 5.0 respectively, and a chord AB of the great circle is tangent to the small circle, then the length of the chord AB is ()


Question: As shown in the figure, circle O is the circumscribed circle of triangle ABC, AD is the diameter of circle O, and EA is the tangent of circle O. If angle EAC = 120.0, then the degree of angle ABC is ()


Question: As shown in the figure, the radius of circle O is 2.0, the distance from point O to line l is 3.0, and point P is a moving point on line l. If PB is tangent to circle O at point B, then the minimum value of PB is ()


Question: As shown in the figure, PA, PB, and CD are the tangents of circle O, A, B, and E are the tangent points, and CD intersects the line segments PA and PB at C and D respectively. If angle APB = 40.0, then the degree of angle COD is ( )


Question: As shown in the figure, AB is the diameter of circle O, point C is on circle O, AE is the tangent of circle O, A is the tangent point, connect BC and extend to intersect AE at point D. If angle AOC = 80.0, then the degree of angle ADB is ()


Question: As shown in the figure, AC is the tangent of circle O, the tangent point is C, BC is the diameter of circle O, AB intersects circle O at point D, and connect OD. If angle BAC = 55.0, then the size of angle COD is ()


Question: As shown in the figure, in triangle ABC, AB = 3.0, AC = 2.0. When angle B is the largest, the length of BC is ()


Question: As shown in the figure, AB is the diameter of the semicircle, point O is the center of the circle, point C is a point on the extended line of AB, and CD is tangent to the semicircle at point D. If AB = 6.0, CD = 4.0, then the value of sinangle C is ()


Question: As shown in the figure, in Rttriangle ABC, angle C = 90.0, angle A = 30.0, BC = 2.0, the radius of circle C is 1.0, point P is the point on the hypotenuse AB, passing point P is a tangent PQ of circle C (Point Q is the tangent point), then the minimum value of the line segment PQ is ()


Question: As shown in the figure, AB and AC are the two chords of circle O. The tangent passing point B and the extended line of OC intersect at point D. If angle D = 36.0, then the degree of angle CAB is ()


Question: As shown in the figure, the diameters of the two concentric circles are 6.0 and 10.0, and a chord AB of the great circle is tangent to the small circle, so the length of the chord AB is ()


Question: As shown in the figure, AP and BP are tangent to circle O at points A and B respectively, angle P = 60.0, point C is on the major arc AB, then the degree of angle C is ()


Question: As shown in the figure, P is a point on the AB extended line of the diameter of circle O, PC is tangent to circle O at C, angle P = 50.0, angle A is ()


Question: As shown in the figure, PA and PB are the tangents of circle O, and the tangent points are A and B. If angle OAB = 30.0, then the degree of angle P is ()


Question: As shown in the figure, PA, PB are circle O is tangent, AC is the diameter of circle O, if angle BAC = 25.0, then angle P is ()


Question: As shown in the figure, the straight line BC is tangent to circle O at point A, AD is the chord of circle O. Connect OD, if angle DAC = 50.0, then the degree of angle ODA is ()


Question: 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 ()


Question: As shown in the figure, AB is the diameter of circle O, CD is tangent to circle O at point D, and the extended line of AB intersects CD at point C, if angle ACD = 40.0, then angle A = ()


Question: As shown in the figure, AB is the diameter of circle O, point D is on the extended line of AB, and DC is tangent to circle O at point C, if angle A = 26.0, then angle D is equal to ()


Question: As shown in the figure, in triangle ABC, AB = AC, angle BAO = 45.0, triangle ABC is inscribed in circle O, D is a point on circle O, passing point D is the tangent of circle O and the extended line of BC at E, if DE perpendicular  BC, AD = 2.0√{2.0}, then the length of DE is ()


Question: As shown in the figure, AB is the tangent of circle O, B is the tangent point, AO and circle O intersect at point C, if angle BAO = 40.0, then the degree of angle OCB is ()


Question: As shown in the figure, circle O ia tangent to AB at point C, angle BCE = 60.0, DC = 6.0, DE = 4.0, then S_triangle CDE is ()


Question: As shown in the figure, AB is tangent to circle O at B, and the secant ACD passes through the center O, if angle BCD = 70.0, then the degree of angle A is ()


Question: As shown in the figure, in triangle ABC, AB = 15.0, AC = 12.0, BC = 9.0, the moving circle passing through point C and tangent to AB intersects CB and CA at points E and F respectively, then the minimum value the length of the line segment EF is ()


Question: As shown in the figure, BC is tangent to circle O at point C, and the extended line of BO intersects circle O at point A, connect AC, if angle ACB = 120.0, then the degree of angle A is equal to ()


Question: As shown in the figure, a quadrilateral green garden, with circular fountains with a radius of 2.0 on all four corners, then the area of the green garden occupied by these four fountains is ()


Question: As shown in the figure, in the square ABCD with edge length 4.0, first draw the arc with point A as the center, the length of AD as the radius, and then draw the arc with the midpoint of the AB side as the center, and half of the AB length as the radius, then the area of the shaded part between the two arcs is () (results remain N_1)


Question: As shown in the figure, in triangle ABC, DE parallel  BC, AE = 3.0, AC = 9.0, AD = 4.0, then the value of AB is ()


Question: As shown in the figure, AB parallel  CD, AD and BC intersect at point O, if AO = 2.0, DO = 4.0, BO = 3.0, then the length of BC is ()


Question: As shown in the figure, given that a parallel  b parallel  c, AB = 1.0, BC = 2.0, EF = 4.0, then DE = ()


Question: As shown in the figure, straight lines a, b, and c intersect straight lines and n at points A, B, C, D, E, and F respectively. Given the straight line a parallel  b parallel  c, if AB = 2.0, BC = 3.0, then the value of frac  DEEF is ()


Question: As shown in the figure, in triangle ABC, DE parallel  BC, if AD = 1.0, DB = 2.0, then the value of frac  AEAC is ()


Question: As shown in the figure, in triangle ABC, M is the midpoint of AC, E is a point on AB, AE=frac {1.0}{4.0}AB, connect EM and extend, and it intersects the extended line of BC at D, then frac  {BC}{CD} = ()


Question: As shown in the figure, in the rectangle ABCD, AB = 3.0, BC = 4.0, point M is on BC, and satisfies BM = 1.0, cross D to make DN perpendicular  AM which intersects AM at point N, then the length of DN is ()


Question: As shown in the figure, in triangle ABC, point D and point E are on AB and BC respectively, and DE parallel  AC, BE = 2.0, CE = 1.0, the area of triangle BDE is 4.0, then the area of triangle ABC is ( )


Question: As shown in the figure, in triangle ABC, DE parallel  BC, if AB = 7.0, AC = 5.0, AD = 3.0, then DE = ()


Question: As shown in the figure, in parallelogram ABCD, point E is on the edge AD, CE intersects BD at point F, if EF = frac {1.0}{3.0}FC, then frac {AE}{ED} = ()


Question: As shown in the figure, given that the point M is the midpoint of edge AB of the parallelogram ABCD, the line segment CM intersects BD at the point E, Striangle BEM = 2.0, then the area of the shaded part in the figure is ()


Question: As shown in the figure, in the quadrilateral ABCD, AD ‖ BC, diagonal AC and BD intersect at O, if \\ frac {s {\triangle ADO} {s {\triangle DOC}} = \frac  {1}{3}


Question: As shown in the figure, in parallelogram ABCD, angle C = 120.0, AB = AE = 5.0, AE and BD intersect at point F, AF = 2 EF. Then the length of BC is ()


Question: As shown in the figure, D and E are the points on the edges AB and AC of triangle ABC, DE parallel  BC, if AD:DB=1.0:3.0, AE = 2.0, then the length of AC is ()


Question: As shown in the figure, given that AB parallel  CD parallel  EF, AD:AF=3.0:5.0,BE=15.0, then the length of CE is equal to ()


Question: As shown in the figure, AD parallel  BE parallel  CF, straight line l2.0, l3.0 and these three parallel lines intersect at points A, B, C, D, E, F, frac {AB}{BC}=frac {2.0}{3.0},DE=6.0, then the value of EF is ( )


Question: As shown in the figure, it is known that a straight line a parallel  b parallel  c, a straight line, n and a, b, c intersect at points A, C, E, B, D, F, if AC = 4.0, AE = 10.0, BD = 3.0, then the value of DF is ()


Question: As shown in the figure, in triangle ABC, DE parallel  BC, if AD = 1.0, DB = 2.0, then the value of frac  ADAB is ()


Question: As shown in the figure, the straight line a parallel  b parallel  c, the straight line, n and a, b, c intersect at the points A, C, E and B, D, F respectively, if AC = 4.0, AE = 10.0, BF =frac {15.0}{2.0}, then the length of DF is ()


Question: As shown in the figure, given that a parallel  b parallel  c, AC = 6.0, AB = 2.0, EF = 5.0, then the value of DF is ()


Question: As shown in the figure, in triangle ABC, DE parallel  BC, frac  {AD}{DB} = frac {1.0}{2.0}, DE = 4.0, then the length of BC is ()


Question: As shown in the figure, in triangle ABC, the points D and E are on the edges AB and AC respectively, DE parallel  BC, given that EC = 6.0, frac {AD}{DB}=frac {2.0}{3.0}, then the length of AE is ()


Question: As shown in the figure, in triangle ABC, D and E are points on AB and AC respectively, which satisfy AD = 3.0, AE = 2.0, EC = 1.0, DE parallel  BC, then AB = ()


Question: As shown in the figure, AB parallel  CD parallel  EF, AC and BD intersect at point E, if CE = 5.0, CF = 4.0, AE = BC, then the value of frac  CDAB is ()


Question: As shown in the figure, in triangle ABC, points D and E are on edges AB and AC respectively, DE parallel  BC. If frac {AE}{AC}=frac {3.0}{4.0},AD=9.0, then AB is equal to ()


Question: As shown in the figure, the straight line l_{1.0}parallel l_{2.0}parallel l_{3.0}, it is known that: AB=4.0,BC=6.0,DE=3.0, then EF = ()


Question: As shown in the figure, in the parallelogram ABCD, F is a point on AB, DF intersects AC at point E, if CD = 10.0, frac {AE}{EC}=frac {2.0}{5.0}, then the length of BF is ()


Question: As shown in the figure, E is a point on AD of the parallelogram ABCD, passing the point E to draw EF parallel  AB and it intersects BD at F, if DE:EA=2.0:3.0,EF=4.0, then the length of CD is ()


Question: As shown in the figure, it is known that l_ 1 parallel  l_ 2 parallel  l_ 3, if AB:BC=2.0:3.0,DE=4.0, then the length of EF is ()


Question: As shown in the figure DE parallel  BC, AD = 3.0, DB = 4.0, AE = 1.5, then EC is equal to ()


Question: As shown in the figure, in triangle ABC, points D and E are on edges AB and AC respectively, DE parallel  BC, and AE = 1.0, AC = 5.0, AB = 6.0, then the length of AD is ()


Question: As shown in the figure, D and E are points on AB and AC of triangle ABC, and DE parallel  BC, if DE:BC=3.0:5.0,AD=6.0, then AB = ()


Question: As shown in the figure, triangle ABC similar  triangle AED, angle ADE = 80.0, angle A = 60.0, then angle B is equal to ()


Question: As shown in the figure, in Rttriangle ABC, angle C = 90.0, BC = 3.0, AC = 4.0, if triangle ABC similar  triangle BDC, then CD = ()


Question: As shown in the figure, triangle ABC similar  triangle DEF, the scale factor of similarity is 1.0:2.0, if EF = 2.0, the length of BC is ()


Question: As shown in the figure, DE is the perpendicular bisector of triangle ABC. Given that the area of triangle ABC is 8.0^2, then the area of triangle ADE is ()^2.


Question: As shown in the figure, D is a point on BC of triangle ABC, it is known that AB = 6.0, AD = 3.0, AC = 4.0, angle DAC = angle B, then the length of BD is ()


Question: As shown in the figure, if triangle ABC similar  triangle ACD, angle A = 60.0, angle ACD = 40.0, then the degree of angle BCD is ()


Question: As shown in the figure, two straight lines are intercepted by three parallel lines, AB = 2.0, BC = 3.0, then frac  EFEG is equal to ()


Question: As shown in the figure, in triangle ABC, DE parallel  BC, if frac {AD}{AB}=frac {1.0}{3.0}


Question: As shown in the figure, C and M are two points on the line segment AB, and the point M is the midpoint of the line segment AC. If AB = 8.0, BC = 2.0, then the length of AM is ()


Question: As shown in the figure, C and D are two points on the line segment AB. If CB = 4.0, DB = 7.0, and D is the midpoint of AC, then the length of AC is equal to ()


Question: As shown in the figure, BC=frac {1.0}{2.0}AB, D is the midpoint of AC, if DC = 3.0, then the length of AB is ()


Question: As shown in the figure, after Xiaolin walks straight in the direction of west from point P 12.0, turns left, the angle of rotation is α, and then walks 12.0, repeating this, Xiaolin has walked 108.0 and returned to point P, then the value of α-5.0 is ()


Question: As shown in the figure, it is known that AD is the midline of triangle ABC, and the perimeter of triangle ABD is 3.0 larger than the perimeter of triangle ACD, then the difference between AB and AC is ()


Question: As shown in the figure, in triangle ABC, AB = AC, M and N are the midpoints of AB and AC respectively, D and E are points on BC. Connect DN, EM. If AB = 13.0, BC = 10.0, DE = 5.0, the area of the shaded part in the figure is 2.0. ()


Question: As shown in the figure, C is a point on the semicircle O with AB as the diameter, connect AC and BC, and make square ACDE and BCFG with AC and BC as the edges respectively. The midpoints of DE, FG, arc \athrAC, arc \athrBC are M, N, P, Q respectively. If MP + NQ = 14.0, AC + BC = 18.0, then the length of AB is ()


Question: As shown in the figure, in the quadrilateral ABCD, point P is the midpoint of the diagonal BD, points E and F are the midpoints of AB and CD respectively, AD = BC, angle FPE = 136.0, then the degree of angle PFE is ()


Question: As shown in the figure, it is known that the straight line a parallel  b parallel  c and the straight line d are perpendicular to them and intersect at the three points A, B and C. If AB = 3.0 and AC = 8.0, the distance between the parallel lines b and c is ( )


Question: As shown in the figure, it is known that angle 1 + angle 2 = 100.0, then angle 3 = ().


Question: As shown in the figure, there is a pond. To measure the distance between A and B at both ends of the pond, firstly take a point C on the flat ground that can directly reach points A and B without passing through the pond, connect AC and extend to D, so that CD = CA , Connect BC and extend to E, make CE = CB, connect ED. If DE = 58.0 is measured, then the distance between A and B is ()


Question: As shown in the figure, the parallel lines a and b are intercepted by the straight line c. If angle 1 = 50.0, then the degree of angle 2 is ()


Question: As shown in the figure, it is known that angle 1 = 60.0, angle A + angle B + angle C + angle D + angle E + angle F = ()


Question: As shown in the figure, in the isosceles triangle ABC, AB = AC, BD is the height on AC, if angle A = 36.0, then the size of angle DBC is ()


Question: As shown in the figure, if a parallel  b, angle 1 = 115.0, then angle 2 = ()


Question: As shown in the figure, in triangle ABC, angle A = 80.0. Point D is a point on the extended line of BC, angle ACD = 150.0, then angle B = ()


Question: As shown in the figure, a parallel  b, point B is on the straight line a, and AB perpendicular  BC, angle 1 = 35.0, then angle 2 = ()


Question: As shown in the figure, the line AB and CD intersect at E, and there is a point F on the bisector of angle CEB, FM parallel  AB. When angle 3 = 10.0, the degree of angle F is ()


Question: As shown in the figure, it is known that straight lines a and b are intercepted by straight line c. If a parallel  b, angle 1 = 120.0, then the degree of angle 2 is ()


Question: As shown in the figure, C and D are two points on circle O with the line segment AB as the diameter. If CA = CD, and angle CAB = 25.0, then the degree of angle ACD is ()


Question: As shown in the figure, AB parallel  EF, CD perpendicular  EF at point D, if angle BCD = 140.0, then the degree of angle ABC is ()


Question: As shown in the figure, in triangle ABC, angle B = 40.0, passing point C to draw CD parallel  AB, angle ACD = 65.0, then the degree of angle ACB is ()


Question: Place a pair of right triangle plates as shown in the figure, so that the leg of the triangle plate with angle 30.0 and the leg of the triangle plate with angle 45.0 are on the same straight line, then the degree of angle 1 is ()


Question: Given the straight line a parallel  b, a right triangle plate is placed as shown in the figure, if angle 1 = 37.0, then the degree of angle 2 is ()


Question: As shown in the figure, the diagonal AC and BD of the rectangle ABCD intersect at point O, CE parallel  BD, DE parallel  AC, if AB = 4.0, BC = 3.0, then the perimeter of the quadrilateral CODE is ()


Question: As shown in the figure, put the right-angled vertex of the triangle plate with 30.0 angle on one side of the ruler, if angle 1 = 35.0, then the degree of angle 2 is ()


Question: As shown in the figure, in parallelogram ABCD, F is a point on AD, CF = CD. If angle B = 72.0, then the degree of angle AFC is ()


Question: From a corner of the cubic blank with edge length 4.0, excavate a small cube with edge length 2.0 to obtain a part as shown in the figure, then the surface area of this part is ()


Question: As shown in the figure, the points B, O, D are on the same straight line, if angle 1 = 15.0, angle 2 = 105.0, then the degree of angle AOC is ()


Question: As shown in the figure, the right-angled vertices of the two triangle plates are overlapped and stacked together. If angle 1 = 40.0, then the degree of angle 2 is ()


Question: As shown in the figure, after a car has turned twice through a section of road, it is the same as the original driving direction, that is, the two roads before and after turning are parallel to each other. The first turning angle angle B is equal to 142.0, and the degree of angle the second turning angle C is ()


Question: As shown in triangle ABC, angle ACB = 90.0, AD bisects angle BAC and it intersects BC at D, DE is perpendicular to AB to E, if DE = 1.5, BD = 3.0, then BC = ()


Question: As shown in the figure, AB = AC, AD = AE, angle BAC = angle DAE, angle 1 = 25.0, angle 2 = 30.0, then angle 3 = ()


Question: As shown in the figure, in triangle ABC, angle B = 46.0, angle C = 54.0, AD bisects angle BAC and it intersects BC at D, then the size of angle BAD is ()


Question: As shown in the figure, it is known that D is a point on BC, angle B = angle 1, angle BAC = 78.0, then angle 2 = ()


Question: As shown in the figure, in triangle ABC, angle ACB = 90.0, fold triangle CBD along CD so that point B falls exactly at point E on the edge of AC. If angle A = 24.0, then the degree of angle BDC is ()


Question: As shown in the figure, DE is the perpendicular bisector of BC of triangle ABC, and it intersects BC at E as well as intersects AB at D, and angle B = 40.0, angle A = 60.0, then the degree of angle ACD is ()


Question: As shown in the figure, in circle O with radius 5.0, AB is a chord, OC perpendicular  AB at point C, and OC = 3.0, then the value of AB is ()


Question: As shown in the figure, in circle O, OA perpendicular  OB, angle A = 35.0, then the degree of arc CD is ()


Question: As shown in the figure, in triangle ABC, DE is the perpendicular bisector of AC, AE = 3.0, the perimeter of triangle ABD is 13.0, then the perimeter of triangle ABC is ()


Question: As shown in the figure, ⊿ABC is inscribed in circle O, if angle OAB = 28.0, then the size of angle C is ()


Question: As shown in the figure, it is known that PA and PB are the tangents of circle O, A and B are the tangent points, AC is the diameter of circle O, angle P = 40.0, then the degree of angle BAC is ()


Question: As shown in the figure, in Rttriangle ABC, angle B = 90.0, AB = 6.0, AC = 10.0 Fold triangle ABC along ED to make point C coincide with point A, then the perimeter of triangle ABE is equal to ()


Question: As shown in the figure, a rectangular ruler is broken and dislocated along a straight line, and points E, D, B, and F are on the same straight line. If angle ADE = 125.0, then the degree of angle DBC is ()


Question: As shown in the figure, the central angle angle AOB = 60.0 ∘, then the degree of the angle of circumference angle ACB is ()


Question: As shown in the figure, in triangle ABC, angle A = 90.0, AB = AC, BD bisects angle ABE, DE perpendicular  BC, if BC = 10.0, then the perimeter of triangle DEC is ()


Question: As shown in the figure, the perpendicular bisector of the isosceles trapezoid ABCD circumscribed by the circle EF = 15.0, then the perimeter of the isosceles trapezoid ABCD is equal to ()


Question: As shown in the figure, if CB = 4.0, DB = 7.0, and D is the midpoint of AC, then the length of AC is ()


Question: As shown in the figure, in triangle ABC, angle ABC = 120.0, if DE and FG bisect AB and BC perpendicularly, then the degree of angle EBF is ()


Question: As shown in the figure, in Rttriangle ABC, angle BAC = 90.0, rotate triangle ABC clockwise around point A by 90.0 to obtain triangle AB′C′ (the corresponding point of point B is point B′, and the corresponding point of point C is point C ′), connect CC′, if angle CC′B′ = 33.0, then the size of angle B is ()


Question: As shown in the figure, point C is on line AB, point D is the midpoint of AC, if CD = 3.0, AB = 10.0, then the length of BC is ()


Question: As shown in the figure, AD is the midline of triangle ABC, and it is known that the perimeter of triangle ABD is 22.0, and AB is longer than AC by 3.0, then the perimeter of triangle ACD is ()


Question: As shown in the figure, the line segment AB = 20.0, C is the midpoint of AB, D is the point on CB, E is the midpoint of DB, and EB = 3.0, then CD is equal to ()


Question: As shown in the figure, C and D are two points on the line segment AB. If CB = 4.0, DB = 7.0, and D is the midpoint of AC, then AB = ()


Question: As shown in the figure, a supermarket shopping cart is placed on a horizontal ground, and its lateral quadrilateral ABCD is in the same plane as a horizontal line on the ground, and AB parallel  l, if angle A = 93.0, angle D = 111.0, then the degree of the acute angle between the straight line CD and l is ()


Question: As shown in the figure, in triangle ABC, angle B = angle C, D is a point on edge BC, point E is on edge AC, angle ADE = angle AED, if angle BAD = 24.0, then angle CDE = ()


Question: As shown in the figure, AB is the chord of circle O, OC perpendicular  AB at point D, and it intersects circle O at point C, if the radius is 5.0, OD = 3.0, then the length of chord AB is ()


Question: As shown in the figure, AB is the diameter of circle O, O is the center of the circle, the chord CD perpendicular  AB at E, AB = 10.0, CD = 8.0, then the length of OE is ()


Question: As shown in the figure, the radius of circle O is OA = 5.0, and the arc with A as the center and OA as the radius intersects circle O at the two points B and C, then the length of the chord BC is equal to ()


Question: As shown in the figure, C and D are two points on the line segment AB. If BC = 3.0, BD = 5.0, and D is the midpoint of AC, then the length of AC is ()


Question: As shown in the figure, in circle O, AB is the chord, OC perpendicular  AB, the foot of perpendicular is C, if AB = 16.0, OC = 6.0, then the diameter of circle O is equal to ()


Question: As shown in the figure, in the circle O with a radius of 10.0, the radius OC is perpendicular to the chord AB to the point D, AB = 16.0, then the length of CD is ()


Question: As shown in the figure, P is a point on the chord AB of circle O, AB = 10.0, AP = 4.0, OP = 5.0, then the radius of circle O is. ()


Question: As shown in the figure, the rectangle intersects with circle O, if AB = 4.0, BC = 5.0, DE = 3.0, then the length of EF is ()


Question: As shown in the figure, AB is the diameter of circle O, CD is the chord, AB perpendicular  CD, the foot of perpendicular is point E, connect OD, CB, AC, angle DOB = 60.0, EB = 2.0, then the length of CD is ()


Question: As shown in the figure, AB is the diameter of circle O, CD is the chord, AB perpendicular  CD at point E, if the radius is 5.0, OE = 3.0, then the length of CD is ()


Question: As shown in the figure, in the circle O with a radius of 5.0, the length of the chord AB is 8.0, then the distance from the center O to the chord AB is ()


Question: As shown in the figure, AB = 8.0, AD = BC = 5.0, then CD is equal to ()


Question: As shown in the figure, C and D are two points on the line segment AB. If CB = 4.0, DB = 7.0, and D is the midpoint of AC, then the length of AB is equal to ()


Question: As shown in the figure, point C is on line AB, point E is the midpoint of AC, and point D is the midpoint of BC. If ED = 6.0, the length of the line segment AB is ()


Question: As shown in the figure, it is known that angle 1 = 40.0, angle A + angle B = 140.0, then the degree of angle C + angle D is ()


Question: As shown in the figure, the diagonals of the quadrilateral ABCD AC perpendicular  BD, the foot of perpendicular is O, and AC = 12.0, BD = 9.0, then the area of the quadrilateral ABCD is ()


Question: As shown in the figure, it is known that triangle ABC, point D is on the extended line of BC, angle ACD = 140.0, angle ABC = 50.0, then the size of angle A is ()


Question: As shown in the figure, point O is on the straight line AB, if angle 2 = 140.0, then the degree of angle 1 is ()


Question: As shown in the figure, line segment AB = 10.0, M is the midpoint of line segment AB, C is the midpoint of line segment MB, N is a point of line segment AM, and MN = 1.0, the length of line segment NC ()


Question: Suppose BF intersects AC at point P, AE intersects DF at point Q. If angle APB = 126.0, angle AQF = 100.0, then angle A-angle F = ()


Question: As shown in the figure, BD and CE are the height and angular bisector of triangle ABC respectively, and they intersect with point O. If angle BCA = 70.0, then the degree of angle BOE is ()


Question: As shown in the figure, it is known that points A, B, and C are on the same straight line, AB = 7.0, BC = 3.0, point D is the midpoint of line segment AC, and the length of line segment DB is ()


Question: As shown in the figure, in the quadrilateral ABCD, the angular bisector of angle DAB and the bisector of exterior angle of angle ABC intersect at point P, and angle angle D + angle C = 200.0, then angle P = ()


Question: As shown in the figure, BP bisects angle ABC and it intersects CD at point F, DP bisects angle ADC and it intersects AB at point E, if angle A = 40.0, angle P = 38.0, then the degree of angle C is ()


Question: As shown in the figure, extend the line segment AB to C with the length of 8.0, so that BC = 4.0, M and N are the midpoints of AB and BC respectively, then the length of MN is ()


Question: As shown in the figure, the four points A, B, C, and D are all on circle O, angle BOD = 110.0, then the degree of angle BCD is ()


Question: As shown in the figure, the quadrilateral ABCD is an inscribed quadrilateral of circle O, angle BCD = 110.0, then the degree of angle BOD is ()


Question: As shown in the figure, a cargo ship sails from point A to point D in the east direction at a speed of 24.0 nautical mile/hour. At point A, a certain island C is measured in the direction 60.0 east by north. The cargo ship arrived at point B after sailing for 30.0 minutes. At this time, it was measured that the island is in the direction 30.0 east by north. Then the shortest distance between the cargo ship and the island C is ()


Question: As shown in the figure, PA, PB are tangent to circle O at points A, B, point C is a point on circle O, and angle P = 36.0, then angle ACB = ()


Question: As shown in the figure, PA and PB are tangent to circle O at A and B respectively, angle C = 55.0, then angle P is equal to ()


Question: As shown in the figure, in a square grid with edge length 1.0. Connect grid points D, N and E, C, DN and EC intersect at point P, then tanangle CPN is ()


Question: As shown in the figure, in Rttriangle ABC, angle C = 90.0, AB = 10.0, AC = 8.0, then sinB is equal to ()


Question: As shown in the figure, the quadrilateral ABCD is the circumscribed quadrilateral of circle O, and AB = 10.0, CD = 12.0, then the perimeter of the quadrilateral ABCD is ()


Question: It is known that for a horizontally placed cylindrical drainage pipe, the radius of the pipe section is 1.0, if the water surface is high 0.2. Then the width of the water surface of the drainage pipe section is ()


Question: As shown in the figure, A, B, C are the three points on circle O, AB, AC are on the both sides of the center O, if angle ABO = 20.0, angle ACO = 30.0, then the degree of angle BOC is ()


Question: As shown in the figure, in the rectangular coordinate system xOy, point A is on the positive semi-axis of the y-axis, points B and C are on the positive semi-axis of x, and angle BAC = angle ACB = 30.0, AC = 4.0, point D is a moving point on the x-axis, the symmetrical points of point D with respect to the straight lines AB and AC are E and F, then the minimum value of the line segment EF is equal to ()


Question: As shown in the figure, angle BAC = 110.0, if A and B are symmetrical with respect to the line MP, A and C are symmetrical with respect to the line NQ, then the size of angle PAQ is ()


Question: As shown in the figure, AB parallel  CD, BE perpendicularly bisects AD, DC = BC, if angle A = 70.0, then angle C = ()


Question: As shown in the figure, in triangle ABC, AB = 10.0, AC = 18.0, point M starts from point A and moves to point B at a speed of 2.0 per second, and point N starts from point C and moves to point A at a speed of 3.0 per second. One of the moving points reaches the endpoint, and the other moving point also stops. When triangle AMN is an isosceles triangle with MN as the base, the movement time is ()


Question: As shown in the figure, in triangle ABC, angle ABC = 110.0, AM = AN, CN = CP, then angle MNP = ()


Question: As shown in the figure, it is known that the bisectors of the four inner corners of parallelogram ABCD intersect at points E, F, G, and H respectively. Connect AC. If EF = 2.0, FG = GC = 5.0, then the length of AC is ()


Question: As shown in the figure, parallelogram ABCD, points E and F are on AD and AB respectively, and connect EB, EC, FC, and FD in turn. The area of the shaded part in the figure is S~ 1 ~, S~ 2 ~, S~ 3 ~ , S~ 4 ~, S~ 1 ~ = 1.0, S~ 2 ~ = 2.0, S~ 3 ~ = 3.0, then the value of S~ 4 ~ is ()


Question: As shown in the figure, in parallelogram ABCD, the diagonal AC and BD intersect at point O, and points E and F are the midpoints of AB and AO respectively. Connect EF. If EF = 3.0, the length of BD is ()


Question: As shown in the figure, parallelogram ABCD's diagonal AC, BD intersect at O, EF passes through point O, and intersects AD, BC at E, F respectively. It is known that the area of parallelogram ABCD is 20.0 ^2.0, then the area of the shaded part in the figure is ()


Question: As shown in the figure, in parallelogram ABCD, the bisector of angle BCD intersects AD at point E, and it intersects the extended line of BA at point F, BF = 4 AF, BC = 12.0, then the length of AF is ()


Question: As shown in the figure, in parallelogram ABCD, AB = 10.0, AD = 15.0, AC and BD intersect at point O. OE perpendicular  BD and it intersects AD at E, then the perimeter of triangle ABE is ()


Question: As shown in the figure, in the parallelogram ABCD, E and F are the midpoints of AD and BC respectively, P is the moving point on the edge DC, G and H are the midpoints of PE and PF respectively, it is known that DC = 10.0, then length of GH is ()


Question: As shown in the figure, in the parallelogram ABCD, the diagonals AC and BD intersect at the point O, and the point E is the midpoint of CD. Connect OE. If the perimeter of the parallelogram ABCD is 24.0 and BD = 8.0, then the perimeter of triangle DOE is ()


Question: As shown in the figure, in the parallelogram ABCD, point E is a point on AB. Connect DE and CE. If DE and CE are the angular bisectors of angle ADC and angle BCD, and AB = 4.0, then the perimeter of the parallelogram ABCD is ()


Question: As shown in the figure, make three parallel lines through a point in the triangle. If the perimeter of the triangle is 6.0, then the sum of the perimeters of the three shaded triangles in the figure is ()


Question: As shown in the figure, in triangle ABC, the straight line DE parallel BC, angle ABC, angle ACB passing through the vertex A intersects DE at points E and D, respectively. If AC = 3.0, AB = 4.0, then the length of DE is ()


Question: As shown in the figure, in triangle ABC, angle B = angle C, D is on BC, angle BAD = 50.0, AE = AD, then the degree of angle EDC is ()


Question: As shown in the figure, in the quadrilateral ABCD, AD parallel  BC, BF bisects angle ABC and it intersects AD at point F, CE bisects angle BCD, and it intersects AD at point E, AB = 8.0, CD = 6.0, EF = 2.0, then the length of AD is ()


Question: As shown in the figure, in triangle ABC, AB = 10.0, AC = 6.0, the straight line DE parallel  CB passing through point A, the bisectors of angle ABC and angle ACB intersect DE at E, D respectively, then the length of DE is ()


Question: As shown in the figure, it is known that the length of one waist AB of the isosceles triangle ABC is 4.0 centimetres. Cross any point D on the bottom edge BC to draw two waist parallel lines, and they intersect the two waists at E and F respectively, then the perimeter of the quadrilateral AEDF is ()


Question: As shown in the figure, in the equilateral triangle ABC, BD bisects angle ABC and it intersects AC at point D, and cross D to draw DE perpendicular  BC at point E, and CE = 1.5, then the length of AB is ()


Question: A ship departs from point A on the sea level and travels 40.0 nautical miles to the west by south direction 40.0 to point B, and then travels 40.0 nautical miles from point B to the west by north 20.0 direction to point C, then the distance between A and C is ( )


Question: As shown in the figure, there is the "herringbone" steel frame, where the inclined beam AB = AC, the top angle angle BAC = 120.0, the span BC = 10.0, AD is the pillar (ie the center line of the bottom BC), two support frames DE perpendicular  AB, DF perpendicular  AC, then DE + DF is equal to ()


Question: Translate triangle ABC to the right along CB to get triangle DEF. If the area of the quadrilateral ABED is equal to 32.0, the translation distance is equal to ()


Question: As shown in the figure, in triangle ABC, angle ACB = 90.0, angle ABC = 60.0, BD bisects angle ABC, P point is the midpoint of BD, if BD = 6.0, the length of CP is ()


Question: As shown in the figure, the height of the floor of a truck compartment from the ground is frac {3.0}{2.0}. In order to facilitate the loading, a wooden board is often used to form an inclined plane. If the angle between the inclined plane and the horizontal ground is not greater than 30.0, the length of this wooden board is at least ( )


Question: As shown in the figure, in Rttriangle ABC, angle ACB = 90.0, AC = 6.0, BC = 8.0, AD is the bisector of angle BAC. If P and Q are the moving points on AD and AC respectively, then the minimum value of PC + PQ is ()


Question: As shown in the figure, in the quadrilateral ABCD, angle BAD = 130.0, angle B = angle D = 90.0, points E and F are the moving points on the line segments BC and DC, respectively. When the perimeter of triangle AEF is the smallest, then the degree of angle EAF is ()


Question: As shown in the figure, the perimeter of triangle ABC is 16.0. Point D is the midpoint of the AB, BD = 2.0, passing point D is the vertical line l of AB, and E is any point on l, then the minimum perimeter of triangle AEC is ()


Question: As shown in the figure, OA and OB are the perpendicular bisectors of the line segments MC and MD respectively, MD = 5.0, MC = 7.0, CD = 10.0, a small ant starts from point M and climbs to any point E on OA, and then climbs to any point F on OB , and then climbs back to point M, the shortest path the little ant crawls can be ()


Question: As shown in the figure, in triangle ABC, BF bisects angle ABC, crossing point A to draw AF perpendicular  BF, the foot of perpendicular is F and extend BC to point G, D is the midpoint of AB. Connect DF and extend to intersect AC at point E. If AB = 12.0, BC = 20.0, then the length of the line segment EF is ()


Question: As shown in the figure, in triangle ABC, points D and E are the midpoints of AB and AC respectively. If DE = 1.5, the length of BC is ()


Question: As shown in the figure, in triangle ABC, BD and CE are angular bisectors, AM perpendicular  BD at point M, AN perpendicular  CE at point N. The perimeter of triangle ABC is 30.0, BC = 12.0. Then the length of MN is ()


Question: As shown in the figure, in triangle ABC, D and E are the midpoints of BC and AC respectively. BF bisects angle ABC and intersects DE at point F. If BC = 6.0, then the length of DF is ()


Question: The students have all played the game of seesaw. The picture is a schematic diagram of a seesaw. The column OC is perpendicular to the ground, OA = OB. When one end of the seesaw A touches the ground, angle AOA′ = 50.0, then when the other end B of the seesaw touches the ground, angle COB′ is equal to ()


Question: As shown in the figure, in triangle ABC, AB = AC, angle A = 40.0, DE bisects AC perpendicularly, then the degree of angle BCD is equal to ()


Question: As shown in the figure, PA and PB are two tangents of circle O with radius 1.0, points A and B are tangent points respectively, angle APB = 60.0, OP intersects chord AB at point C, and intersects circle O at point D. Then the area of the shaded part in the figure is ()


Question: As shown in the figure, in triangle ABC, angle A = 90.0, AB = AC = 3.0, now rotate triangle ABC anticlockwise around point B by a certain angle, point C′ falls on the straight line where the height of side BC is located, then the area swept by BC during the rotation of edge BC is ()


Question: As shown in the figure, the sector OAB and the sector OCD whose central angles are all 90.0 are stacked together, OA = 3.0, OC = 1.0, respectively connect AC and BD, then the area of the shaded part in the figure is ()


Question: As shown in the figure, in order to green the environment, four sector open spaces with a radius of 1.0 are drawn at the four corners of the rectangular open space for greening, then the total green area is ()


Question: The lateral surface of a staircase is shown in the figure. The measured length of AB is 3.0, and the slope ratio of the stair slope BC is 1.0:2.0, then the length of the slope BC of the staircase is ()


Question: At a certain moment, there is a passenger ship at sea point P, and lighthouse A is measured in the direction 30.0 north by east of P, and is 50.0 nautical miles away. The passenger ship sails at the speed of 60.0 nautical mile/hour in the direction of 60.0 from north by west for $frac {2.0}{3.0}$hours to reach point B, then tanangle BAP = ()


Question: As shown in the figure, it is known that there is a laser auxiliary signal within a certain range of the lighthouse M. A ship is sailing at a constant speed from south by north at a constant speed at sea. The ship measured at A and measured that the lighthouse M was in the direction 30.0 to the east by north, and it traveled 1.0. Arrived at point B after hours, and just entered the laser signal area of lighthouse M at this time. It is measured that lighthouse M is in the direction of 45.0 east by north, then the time for the ship to pass the laser signal area of lighthouse M is ()


Question: As shown in the figure, at 8.0 in the morning, a ship departs from point A and sails northward at a speed of 15.0 nautical miles/hour, and arrives at point B at 9.0 and 40.0 minutes. From point A, lighthouse C is measured in the direction 26.0 west by north. From point B, lighthouse C is measured in the 52.0 direction west of north, then the distance from point B to lighthouse C is ()