Circle + triangle - examples

  1. RT - inscribed circle
    rt_incircle In a rectangular triangle has sides lengths> a = 30cm, b = 12.5cm. The right angle is at the vertex C. Calculate the radius of the inscribed circle.
  2. 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.
  3. 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?
  4. Rectangle
    rectangle_inscribed_circle The rectangle is 11 cm long and 45 cm wide. Determine the radius of the circle circumscribing rectangle.
  5. Square and circles
    kruznica_stvorec_1 Square with sides 61 mm is circumscribed and inscribed with circles. Determine the radiuses of both circles.
  6. 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.
  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. Described
    desc_circle Calculate perimeter of the circle described by a triangle with sides 478, 255, 352.
  9. Equilateral triangle
    3angle_in_circle How long should be the minimum radius of the circular plate to be cut equilateral triangle with side 7 mm from it?
  10. Hexagon A
    hexagon Calculate area of regular hexagon inscribed in circle with radius r=9 cm.
  11. OK circle
    circles2 Calculate the radius (circumradius) of the circle described right triangle with hypotenuse long 33 and one cathetus long 17.
  12. n-gon II
    x-gon_1 What is the side length of the regular 5-gon circumscribed circle of radius 11 cm?
  13. Circle section
    circle_segment Equilateral triangle with side 33 is inscribed circle section whose center is in one of the vertices of the triangle and the arc touches the opposite side. Calculate: a) the length of the arc b) the ratio betewwn the circumference to the circle sector.
  14. 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°?
  15. n-gon
    x-gon What is the side length of the regular 5-gon inscribed in a circle of radius 12 cm?
  16. Track arc
    krizenie Two straight tracks is in an angle 74°. They will join with circular arc with radius r=1127 m. How long will be arc connecting these lines (L)? How far is the center point of arc from track crossings (x)?
  17. V-belt
    v_belt Calculate the length of the belt on pulleys with diameters of 105 mm and 393 mm at shaft distance 697 mm.
  18. Triangle in circle
    triangle_in_circle Vertices of the triangle ABC lies on a circle with radius 3 so that it is divided into three parts in the ratio 4:4:4. Calculate the circumference of the triangle ABC.
  19. EQL triangle
    rs_triangle Calculate inradius and circumradius of equilateral triangle with side a=77 cm.
  20. Shooter
    terc_1 The shooter fired to a target from distance 11 m The individual concentric circle of targets have a radius increments 1 cm (25 points) by 1 point. Shot was shifted by 8'(angle degree minutes). How many points should win his shot?

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