Planimetrics - math word problems - page 146 of 185
Number of problems found: 3688
- Sum of inner angles
Prove that the sum of all inner angles of any convex n-angle equals (n-2).180 degrees. - Proof I
When added to the product of two consecutive integers larger one, we get the square larger one. Is this true or not? - Ball Velocity Train Relative
We throw a ball in an express car traveling at a constant speed of 24 m/s, whose initial speed relative to the vehicle is 7 m/s. What is the initial velocity of the ball relative to the surface of the ground if we throw it a) in the direction of travel b) - Right-angled triangle
The right-angled triangle XYZ is similar to the triangle ABC, which has a right angle at the vertex X. The following applies: side a = 9 cm, x=4 cm, x = v-4 (v = height of triangle ABC). Calculate the unknown side lengths of both triangles. - Probability - triangles
We have five lines with lengths of 3cm, 5cm, 7cm, 9cm, and 11cm. What is the probability that we will be able to construct a triangle with randomly selected three? - 2d shape
Calculate the area of a shape in which an arbitrary point is not more than 3 cm from the segment AB. The length of segment AB is 5 cm. - Circle point equation
Determine the equation of the circle that is the set of all points of the plane that are twice as far from the point [3,7] as they are from the point [0,1]. - Hypotenuse - RT
A triangle has a hypotenuse of 55 and an altitude to the hypotenuse of 33. What is the area of the triangle? - Two people
Two straight lines cross at right angles. Two people start simultaneously at the point of intersection. John walks at the rate of 4 kph on one road, and Jenelyn walks at the rate of 8 kph on the other road. How long will it take for them to be 20√5 km apa - Rhombus construct
Construct parallelogram (rhombus) ABCD, | AB | = 4 cm alpha = 30° and | BD | = 5 cm. - Observatories A,B
The target C is observed from two artillery observatories, A and B, 296 m apart. At the same time, angle BAC = 52°42" and angle ABC = 44°56". Calculate the distance of the target C from observatory A. - Similarity
Are two right triangles similar if the first one has an acute angle 60° and the second one has an acute angle 30°? - Candy - MO
Gretel deploys different numbers to the vertex of a regular octagon, from one to eight candy. Peter can then choose which three piles of candy to give Gretel others retain. The only requirement is that the three piles lie at the vertices of an isosceles t - Boat in the lake
A boatman walks along the ship's deck at a constant speed of 5 km/h in a direction that forms an angle of 60° with the direction of the ship's speed. The boat moves with respect to the lake's calm surface at a constant speed of 10 km/h. Determine graphica - Triangle construction
Construct a triangle ABC if you know the lengths of its sides c = 5 cm, a = 4 cm and angle ABC is 60°. Measure the length of side b in millimeters. Side length b is: a, 75 mm < b < 81 mm b, 53 mm < b < 59 mm c, 43 mm < b < 49 mm d, 13 mm - Circle - analytics geometry Write the equation of the circle that passes through the points Q[3.5] R[2.6] and has its center on the line 2x+3y-4=0.
- Reconstruction of the corridor
Calculate how many minutes will be reduced to travel a 213 km long railway corridor, where the maximum speed increases from 120 km/h to 160 km/h. Calculate how many minutes will shorten travel time if we consider that the train must stop at 6 stations. Ea - Line segments
Triangle ABC is divided by line segments. Lines DE and AB are parallel. Two lines are drawn from vertex C. The first line intersects points H and F on segments DE and AB. The second line intersects points I and G on segments DE and AB. Triangles CDH, CHI, - Trapezoid angles
Given an isosceles trapezoid ABCD, in which | AB | = 2 | BC | = 2 | CD | = 2 | DA | holds. On its side BC, the point K is such that | BK | = 2 | KC |; on its CD side, the point L is such that | CL | = 2 | LD |, and on its DA side, the point M is such that - Circle distance ratio
What is the ratio of the distance of the nearest and farthest point of the circle described by the equation x2+y2-16x-12y+75=0 from the origin of the coordinate system?
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