Geometry - problems

  1. Sphere equation
    sphere2 Obtain the equation of sphere its centre on the line 3x+2z=0=4x-5y and passes through the points (0,-2,-4) and (2,-1,1).
  2. Equation of circle 2
    circle_axes Find the equation of a circle which touches the axis of y at a distance 4 from the origin and cuts off an intercept of length 6 on the axis x.
  3. Forces
    ijk In point X acts three orthogonal forces: F1 = 13 N, F2 = 8 N and F3 = 15 N. Determine the resultant of F and the angles between F and forces F1, F2 and F3.
  4. Reverse Pythagorean theorem
    pytagors Given are lengths of the sides of the triangles. Decide which one is rectangular: Δ ABC: 73 m, 66 m, 51 m ? Δ DEF: 63 cm, 105 cm, 84 cm ? Δ GHI: 50 dm, 48 dm, 14 dm ? Δ JKL: 31 m, 45 m, 40 m ? Δ MNO: 28 m, 53 m, 45 m ?
  5. Triangle
    sedlo Triangle KLM is given by plane coordinates of vertices: K[-19, -8] L[8, -12] M[2, -6]. Calculate its area and itsinterior angles.
  6. Railways
    railways Railways climb 5.8 ‰. Calculate the height difference between two points on the railway distant 2389 meters.
  7. Circular pool
    arc_open The base of pool is circle with a radius r = 10 m excluding circular segment that determines chord length 10 meters. Pool depth is h = 2m. How many hectoliters of water can fit into the pool?
  8. Similarity
    similar_triangle Are two right triangles similar to each other if the first one has a acute angle 10° and second one has acute angle 50°?
  9. Hexagon
    hexagon There is regular hexagon ABCDEF. If area of the triangle ABC is 19, what is area of the hexagon ABCDEF? I do not know how to solve it simply....
  10. Climb
    Mazda_RX7_1 On the road sign, which informs the climb is 20%. Car goes 5 km along this road. What is the height difference that car went?
  11. Similarity coefficient
    eqlateral_triangles The ratio of similarity of two equilateral triangles is 3.9 (ie 39:10). The length of the side of smaller triangle is 3 cm. Calculate the perimeter and area of ​​the larger triangle.
  12. Speed of Slovakian trains
    zssk_train Rudolf decided to take the train from the station 'Nová Baňa' to 'Gelnica'. In the train timetables found train R 371 Horehronec : km0Břeclav os.n.05:268Lanžhot05:3205:3214Brodské05:3705:3818Kúty05:4205:4344Malacky05:5906:0082Bratislava hl.st.06:2606:37
  13. Center
    triangle_axis Calculate the coordinates of the center of gravity T [x, y] of triangle ABC; A[27,-11] B[2,-30] C[11,12].
  14. Crossroads
    crossroad The rectangular crossroads comes passenger car and an ambulance, the ambulance left. Passenger car is at 45 km/h and ambulance 58 km/h. Calculate such a relative speed of the ambulance moves to the car.
  15. Climb
    scenic_road Road has climbing 1:23. How big is a angle corresponds to this climbing?
  16. OK circle
    circles2 Calculate the radius (circumradius) of the circle described right triangle with hypotenuse long 43 and one cathetus long 21.
  17. Angle between lines
    angle_two_lines Calculate the angle between these two lines: ? ?
  18. Slope
    slope What is the slope of a line with an inclination 52°?
  19. Pentagon
    5gon_1 Within a regular pentagon ABCDE point P is such that the triangle is equilateral ABP. How big is the angle BCP? Make a sketch.
  20. The chord
    Tetiva Side of the triangle inscribed in a circle is a chord passing through circle center. What size are the internal angles of a triangle, if one of them is 40°?

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