Geometry - practice problems
Number of problems found: 1524
- Vector - basic operations
There are given points A [-9; -2] B [2; 16] C [16; -2] and D [12; 18] a. Determine the coordinates of the vectors u=AB v=CD s=DB b. Calculate the sum of the vectors u + v c. Calculate difference of vectors u-v d. Determine the coordinates of the vector w
What is the slope of the perpendicular bisector of line segment AB if A[9,9] and B[9,-2]?
- Chors 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).
- Similar triangles
In the triangle DEF is DE = 21cm, EF = 14.7cm, DF = 28cm. The triangle D´E´F´ is similar to the triangle DEF. Calculate the lengths of the sides of the triangle D´E´F´ if the similarity coefficient is one-seventh.
- 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]?
- The amphitheater
The amphitheater has the shape of a semicircle, the spectators sit on the perimeter of the semicircle, the stage forms the diameter of the semicircle. Which of the spectators P, Q, R, S, T sees the stage at the greatest viewing angle?
- The triangles
The triangles ABC and A'B'C 'are similar with a similarity coefficient of 2. The angles of the triangle ABC are alpha = 35°, beta = 48°. Determine the magnitudes of all angles of triangle A'B'C '.
Calculate distance between two points X[18; 19] and W[20; 3].
- Points collinear
Show that the point A(-1,3), B(3,2), C(11,0) are col-linear.
For vector w is true: w = 2u-5v. Determine coordinates of vector w if u=(3, -1), v=(12, -10)
- Similarity coefficient
The triangles ABC and A "B" C "are similar to the similarity coefficient 2. The sizes of the angles of the triangle ABC are α = 35° and β = 48°. Find the magnitudes of all angles of triangle A "B" C ".
- Find quadrant
On a graph, Point Y is located at (4, -2). Point Z is located 5 units to the left of Point Y. In which quadrant is Point Z located?
Determine coordinates of the vector u=CD if C[19;-7], D[-16,-5].
Determine which type of quadrilateral ABCD is and find its perimeter if you know coordinates of vertices: A/2,4 /, B / -2,1 /, C / -2, -2 /, D/2, -5 /.
- Circle from string
Martin has a long 628 mm string. He makes a circle from it. Calculate the radius of the circle.
- OK circle
Calculate the radius (circumradius) of the circle described right triangle with hypotenuse long 33 and one cathetus long 17.
Find the slope of the line: x=t and y=1+t.
Line segments 62 cm and 2.2 dm long we divide into equal parts which lengths in centimeters is expressed integer. How many ways can we divide?
If the endpoints of a diameter of a circle are A(10, -1) and B (3, 10), what is the radius of the circle?
In the semicircle with center S and the diameter AB is constructed equilateral triangle SBC. What is the magnitude of the angle ∠SAC?