Circle - high school - math problems

Number of problems found: 201

  • Regular octagon pad
    You need to make a pad in the shape of a regular octagon with a side length of 4 cm. What is the minimum diameter of the circle-shaped semi-finished product from which we make the pad, and what will be the percentage of waste? (Round the results to 1 deci
  • Two waves
    Two waves are out of phase by 26°. If the period of the waves is 6 seconds, what is the time difference between the waves? Give your answer in seconds to 2 d. P.
  • Circle inscribed
    There is a triangle ABC and a circle inscribed in this triangle with radius 15. The point T is the point of contact of the inscribed circle with the side BC. What is the area of the triangle ABC if | BT | = 25 a | TC | = 26?
  • Wheel gear
    A drive wheel of radius 2 is connected to a drive wheel of radius 1 by a pulley of length 17. What is the distance between the wheel axles?
  • Tarzan
    Tarzan, weighing m = 90 kg, tries to cross the river by swinging with a vine hanging from a tree leaning over the river. Liana has a length l = 12 m. The speed of the Tarzan in the lowest swing position is v = 8 m/s. Tarzan doesn't know that the liana wil
  • Megapizza
    Megapizza will be divided among 100 people. First gets 1%, 2nd 2% of the remainder, 3rd 3% of the remainder, etc. Last 100th 100% of the remainder. Which person got the biggest portion?
  • Metal washers
    Metal washers with a diameter of 80 mm are cut from a strip of steel sheet with a width of 10 cm and a length of 2 m. Calculate the percentage of material waste if no material is lost when two adjacent circles meet.
  • Constant Angular Acceleration
    The particle began to move from rest along a circle with a constant angular acceleration. After five cycles (n = 5), its angular velocity reached the value ω = 12 rad/s. Calculate the magnitude of the angular acceleration ε of this motion and the time int
  • Five circles
    On the line segment CD = 6 there are 5 circles with a radius one at regular intervals. Find the lengths of the lines AD, AF, AG, BD, and CE.
  • Inscribed and described circle
    Find the radii of a circle inscribed and circumscribed by a regular pentagon whose side measures 3 cm.
  • Ratio of squares
    A circle is given in which a square is inscribed. The smaller square is inscribed in a circular arc formed by the side of the square and the arc of the circle. What is the ratio of the areas of the large and small squares?
  • Pentadecagon
    Calculate the content of a regular 15-sides polygon inscribed in a circle with radius r = 4. Express the result to two decimal places.
  • Two chords
    From the point on the circle with a diameter of 8 cm, two identical chords are led, which form an angle of 60°. Calculate the length of these chords.
  • Circle and square
    An ABCD square with a side length of 100 mm is given. Calculate the radius of the circle that passes through the vertices B, C and the center of the side AD.
  • Five-gon
    Calculate the side a, the circumference and the area of the regular 5-angle if Rop = 6cm.
  • Annulus
    Two concentric circles with radii 1 and 9 surround the annular circle. This ring is inscribed with n circles that do not overlap. Determine the highest possible value of n.
  • The bridge
    A vehicle weighing 5,800 kg passes 41 km/h on an arched bridge with a radius of curvature of 62 m. What force is pushing the car onto the bridge as it passes through the center? What is the maximum speed it can cross over the center of the bridge so that
  • Rotaty motion
    What is the minimum speed and frequency that we need to rotate with water can in a vertical plane along a circle with a radius of 70 cm to prevent water from spilling?
  • Eq triangle minus arcs
    In an equilateral triangle with a 2cm side, the arcs of three circles are drawn from the centers at the vertices and radii 1cm. Calculate the content of the shaded part - a formation that makes up the difference between the triangle area and circular cuts
  • Circular railway
    The railway connects in a circular arc the points A, B, and C, whose distances are | AB | = 30 km, AC = 95 km, BC | = 70 km. How long will the track from A to C?

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Circle Problems. Examples for secondary school students.