Circle - problems

  1. Construct
    inscircle_triangle Construct a triangle ABC inscribed circle has a radius r = 2 cm, the angle alpha = 50 degrees = 8 cm. Make a sketch, analysis, construction and description.
  2. An equilateral
    goat__wolf_and_cabbage_1 An equilateral triangle with a side 10 m represents a wooden platform standing in a lawn. A goat is tied to a corner with a 15 m rope. What is the maximum amount of grazing area available to the goat?
  3. Distance problem
    linear_eq_3 A=(x, x) B=(1,4) Distance AB=√5, find x;
  4. Pavement
    chodnik2 Calculate the length of the pavement that runs through a circular square with a diameter of 40 m if distance the pavement from the center is 15 m.
  5. Quarter circle
    quarter_circle_1 What is the radius of a circle inscribed in the quarter circle with a radius of 100 cm?
  6. Circle annulus
    medzikruzie2 There are 2 concentric circles in the figure. Chord of larger circle 10 cm long is tangent to the smaller circle. What are does annulus have?
  7. Hands
    soviet_watch The clock shows 12 hours. After how many minutes will agle between hour and minute hand 90°? Consider the continuous movement of both hands hours.
  8. Circle chord
    circleChord What is the length d of the chord circle of diameter 36 m, if distance from the center circle is 16 m?
  9. Rectangle
    rectangle_inscribed_circle The rectangle is 11 cm long and 45 cm wide. Determine the radius of the circle circumscribing rectangle.
  10. Clock
    hodiny How many times a day hands on a clock overlap?
  11. Cone A2V
    popcorn Surface of cone in the plane is a circular arc with central angle of 126° and area 415 dm2. Calculate the volume of a cone.
  12. Washer
    pracka Washing machine drum wash at 54 RPM. Washing machine motor pulley has diameter 5 cm. What must be the diameter of the drum machine pulley when the motor is at 301 RPM?
  13. Square and circles
    kruznica_stvorec_1 Square with sides 61 mm is circumscribed and inscribed with circles. Determine the radiuses of both circles.
  14. Rectangle
    diagonal In rectangle with sides 3 and 10 mark the diagonal. What is the probability that a randomly selected point within the rectangle is closer to the diagonal than to any side of the rectangle?
  15. Circles
    two_circles The areas of the two circles are in the ratio 5:14. The larger circle has diameter 23. Calculate the radius of the smaller circle.
  16. MO SK/CZ Z9–I–3
    ball_floating_water John had the ball that rolled into the pool and it swam in the water. Its highest point was 2 cm above the surface. Diameter of circle that marked the water level on the surface of the ball was 8 cm. Determine the diameter of John ball.
  17. Cylinders
    cylinders Area of the side of two cylinders is same rectangle of 50 cm × 11 cm. Which cylinder has a larger volume and by how much?
  18. Circle arc
    pizza Circle segment has a circumference of 41.89 m and 251.33 m2 area. Calculate the radius of the circle and size of central angle.
  19. Rhombus
    rhomus_circle It is given a rhombus of side length a = 29 cm. Touch points of inscribed circle divided his sides into sections a1 = 14 cm and a2 = 15 cm. Calculate the radius r of the circle and the length of the diagonals of the rhombus.
  20. Gear
    ozubene_kolesa Two gears, fit into each other, has transfer 2:3. Centres of gears are spaced 82 cm. What are the radii of the gears?

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