Geometry - problems

  1. Right triangle from axes
    axes2 A line segment has its ends on the coordinate axes and forms with them a triangle of area equal to 36 sq. Units . The segment passes through the point ( 5,2). What is the slope of the line segment. ?
  2. Points collinear
    collinear Show that the point A(-1,3), B(3,2), C(11,0) are col-linear.
  3. Shadow
    shadow_1 A meter pole perpendicular to the ground throws a shadow of 40 cm long, the house throws a shadow 6 meters long. What is the height of the house?
  4. Two chords
    circle_chords There is a given circle k (center S, radius r). From point A which lies on circle k are starting two chords of length r. What angle does chords make? Draw and measure.
  5. Prove
    two_circles_1 Prove that k1 and k2 is the equations of two circles. Find the equation of the line that passes through the centers of these circles. k1: x2+y2+2x+4y+1=0 k2: x2+y2-8x+6y+9=0
  6. Forces
    ijk In point O acts three orthogonal forces: F1 = 20 N, F2 = 7 N and F3 = 19 N. Determine the resultant of F and the angles between F and forces F1, F2 and F3.
  7. Reverse Pythagorean theorem
    pytagors Given are lengths of the sides of the triangles. Decide which one is rectangular: Δ ABC: 77 dm, 85 dm, 36 dm ? Δ DEF: 55 dm, 82 dm, 61 dm ? Δ GHI: 24 mm, 25 mm, 7 mm ? Δ JKL: 32 dm, 51 dm, 82 dm ? Δ MNO: 51 dm, 45 dm, 24 dm ?
  8. Triangle
    sedlo Triangle KLM is given by plane coordinates of vertices: K[-12, -11] L[-15, -18] M[-13, -12]. Calculate its area and itsinterior angles.
  9. Railways
    railways Railways climb 7.4 ‰. Calculate the height difference between two points on the railway distant 3539 meters.
  10. 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?
  11. Similarity
    similar_triangle Are two right triangles similar to each other if the first one has a acute angle 40° and second one has acute angle 50°?
  12. Hexagon
    hexagon There is regular hexagon ABCDEF. If area of the triangle ABC is 22, what is area of the hexagon ABCDEF? I do not know how to solve it simply....
  13. Climb
    Mazda_RX7_1 On the road sign, which informs the climb is 8.7%. Car goes 5 km along this road. What is the height difference that car went?
  14. Similarity coefficient
    eqlateral_triangles The ratio of similarity of two equilateral triangles is 3.5 (ie 7:2). The length of the side of smaller triangle is 2.4 cm. Calculate the perimeter and area of ​​the larger triangle.
  15. Speed of Slovakian trains
    zssk_train Rudolf decided to take the train from the station 'Trnava' to 'Zemianske Kostoľany'. In the train timetables found train R 725 Remata : km0Bratislava hl.st.12:574Bratislava-Vinohrady13:0113:0219Pezinok13:1213:1346Trnava13:3013:3263Leopoldov13:4514:0168H
  16. Center
    triangle_axis Calculate the coordinates of the center of gravity T [x, y] of triangle ABC; A[11,4] B[13,-7] C[-17,-18].
  17. Crossroads
    crossroad The rectangular crossroads comes passenger car and an ambulance, the ambulance left. Passenger car is at 43 km/h and ambulance 52 km/h. Calculate such a relative speed of the ambulance moves to the car.
  18. OK circle
    circles2 Calculate the radius (circumradius) of the circle described right triangle with hypotenuse long 33 and one cathetus long 17.
  19. Climb
    scenic_road Road has climbing 1:27. How big is a angle corresponds to this climbing?
  20. Angle between lines
    angle_two_lines Calculate the angle between these two lines: ? ?

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