Perimeter of Circle Problems - page 12 of 15
Number of problems found: 287
- Z7–I–4 2018 MO Betka
Karel was playing with gears assembled into a gear train. When he turned one wheel, all the others turned too. The first wheel had 32 teeth and the second had 24 teeth. When the third wheel (which is in the middle of the gear train) made exactly eight ful - Triangle - many properties
In a right triangle ABC with a right angle at the vertex C, it is given: a = 17 cm, Vc = 8 cm. Calculate the length of the sides b, c, its area S, the perimeter o, the length of the radii of the circles of the triangle circumscribed by R and inscribed r a - Nonagon
Calculate the area and perimeter of a regular nonagon if its radius of the inscribed circle is r = 10 cm. - Gear train
A gear train is assembled from three gear wheels. The first has 165 teeth, the second 132 teeth, and the third 231, where the second engages with the first and the third with the second. The first and third do not touch. How many times per minute will all - Velocipedes
In the 19th century, bicycles had no chain drive, and the wheel axis connected the pedals directly. This wheel diameter gradually increased until the so-called high bikes (velocipedes) had a front-wheel diameter of up to 1.5 meters, while the rear wheel w - Circular segment
Calculate the area S of the circular segment and the length of the circular arc l. The height of the circular segment is 2 cm, and the angle α = 60°. Help formula: S = 1/2 r². (Β-sinβ) - Two tangents
The figure shows a circle k with centre S and radius 5 cm, and a point A which is 13 cm from centre S. From point A, two tangents p and q are drawn to circle k, with points of tangency P and Q. In addition, another tangent t is drawn to circle k, intersec - Triangle circle calculation
The following elements are known in the right triangle ABC: a = 10 cm, height to side c h = 9.23 cm. Calculate o, R (radius of the inscribed circle), r (radius of the inscribed circle). - Rectangle
In a rectangle with sides 8 and 9, a diagonal is drawn. What is the probability that a randomly selected point inside the rectangle is closer to the diagonal than to any side of the rectangle? - Circle arc
A circular sector has an arc length of 7.16 m and an area of 146.69 m². Calculate the radius of the circle and the size of the central angle. - The amphitheater
The amphitheater has the shape of a semicircle, the spectators sit on the perimeter of the semicircle, and the stage forms the diameter of the semicircle. Which spectators, P, Q, R, S, and T, see the stage at the greatest viewing angle? - Minute hand distance
The distance between the tip of the minute hand and the center of the dial is 12 mm. Determine the distance traveled by the tip in 45 min. (draw a clock face and a minute hand and realize the distance it will cover in 45 min.) - Hexagon in circle
Calculate the radius of a circle whose length is 10 cm greater than the circumference of a regular hexagon inscribed in this circle. - Circle described
The circle radius described in the right triangle with a 6 cm long leg is 5 cm. Calculate the circumference of this triangle. - Outer contact of circles
Construct a circle k1 (S1; 1.5 cm), k2 (S2; 2 cm), and K3 (S3; 2.5 cm) so that they are always two outer contacts. Calculate the perimeter of the triangle S1S2S3. - Three
Three points are given: A (-3, 1), B (2, -4), C (3, 3) a) Find the perimeter of triangle ABC. b) Decide what type of triangle the triangle ABC is. c) Find the length of the inscribed circle - Point distance
Draw the line segment AB, AB = 5 cm. Draw a set of points 2 cm away from line AB. What shape does this set of points form? - Parallelogram perimeter construction
Assembly parallelogram ABCD: AB = 4.8 cm, va = 3 cm, BC = 4 cm. Calculate the circuit. Make a sketch. - Larger perimeter
A square and a circle pass through two adjacent vertices of the square (endpoints of side a) and the center of the opposite side (c). Which of the plane shape has a larger perimeter? - Circle from string
Martin has a long 628 mm string. He makes a circle from it. Calculate the radius of the circle.
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