Planimetrics + line - practice problems - page 2 of 12
Number of problems found: 233
- Isosceles 5575
The picture shows an isosceles triangle VLK with a center of gravity of T. The base VL measures 16 cm, and the line KK1 measures 18 cm. How long is the VV1 line? - Circles
In the circle with a radius, 7.5 cm is constructed of two parallel chords whose lengths are 9 cm and 12 cm. Calculate the distance of these chords (if there are two possible solutions, write both). - Ratio of triangles areas
In an equilateral triangle ABC, the point T is its center of gravity, the point R is the image of the point T in axial symmetry along the line AB, and the point N is the image of the point T in axial symmetry along the line BC. Find the ratio of the areas - Right triangles
How many right triangles we can construct from line segments 3,4,5,6,8,10,12,13,15,17 cm long? (Do not forget the triangle inequality).
- Chords centers
The circle with a diameter 17 cm, upper chord/CD/ = 10.2 cm and bottom chord/EF/ = 7.5 cm. The midpoints of the chords H, G is that/EH/ = 1/2 /EF/and/CG/ = 1/2 /CD/. Determine the distance between the G and H if CD II EF (parallel). - Obtuse angle
Line OH is the height of the triangle DOM, and line MN is the bisector of angle DMO. the Obtuse angle between the lines MN and OH is four times larger than the angle DMN. What size is the angle DMO? (see attached image) - Three points
Three points K (-3; 2), L (-1; 4), M (3, -4) are given. Find out: (a) whether the triangle KLM is right b) calculate the length of the line to the k side c) write the coordinates of the vector LM d) write the directional form of the KM side e) write the d - Touch circle
Point A has a distance (A, k) = 10 cm from a circle k with radius r = 4 cm and center S. Calculate: a) the distance of point A from the point of contact T if the tangent to the circle is drawn from point A b) the distance of the contact point T from the l - The coordinates
The coordinates (5, 2) and (-6, 2) are vertices of a hexagon. Explain how to find the length of the segment formed by these endpoints. How long is the segment?
- Parametric form
Calculate the distance of point A [2,1] from the line p: X = -1 + 3 t Y = 5-4 t Line p has a parametric form of the line equation. - Intersection 6653
Two straight paths cross, making an angle alpha = 53 degrees 30'. There are two pillars on one of them, one at the intersection, the other at a distance of 500m from it. How far does one have to go from the intersection along the other road to see both po - Applies 14683
Point B is the center of the circle. The line AC touches the circles at point C and applies AB = 20 cm and AC = 16 cm. What is the radius of the circle BC? - Calculate 4865
Calculate the length of the line segment AB, given A [8; -6] and B [4; 2] - Chord BC
A circle k has the center at the point S = [0; 0]. Point A = [40; 30] lies on the circle k. How long is the chord BC if the center P of this chord has the coordinates [- 14; 0]?
- Trapezoid thirds
The ABCD trapezoid has parallel sides AB and CD. The E point lies on the AB side. The segment DE divides the trapezoid into two parts with the same area. Find the length of the AE line segment. - Three points 2
The three points are A(3, 8), B(6, 2), and C(10, 2). Point D is such that the line DA is perpendicular to AB, and DC is parallel to AB. Calculate the coordinates of D. - Calculate 8
Calculate the coordinates of point B axially symmetrical with point A[-1, -3] along a straight line p : x + y - 2 = 0. - Triangles 6647
For triangles ABC and A'B'C': alpha = alpha with a line, beta with line = beta. a) are these triangles identical? Why? b) are these triangles similar? Why? - Identical 20963
In which triangles is the line identical with the height?
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