Circle practice problems - page 13 of 51
Number of problems found: 1002
- 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 - Megapizza
Mega pizza 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? - 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 - two spacecraft
Recently, two spacecraft successfully landed on two small planets labeled α and β. Both ships were equipped with sensitive sensors that measured the basic parameters of the asteroids. The sensors found that the day α took six times longer on planet α than - Angles - clock hands
Find the angle that the large hand makes with the small hand of the clock - the central angle at 12:30. Find the magnitude of the smaller angle (if possible). (Help: it's enough if you calculate how big an angle the hands make if they are 1 minute apart. - Two gears
The gearbox will use a large gear to turn a smaller gear. The large gear will make 75 revolutions per minute, while the smaller gear must make 384 revolutions per minute. Find the smallest number of teeth each gear could have. [Hint: Use either GCF or LCM - True and false
A circle k(S; 8 cm) is given. Furthermore, points K, L are given such that the following holds: the length of SL is 6 cm, the length of SM is greater than 8 cm. Which of the following statements is not true a. The circle m(M; |ML|) has exactly two common - Lake path calculation
Lake Trasimeno is approximately in the shape of a circle, its area is about 28 square kilometers, and Mr. Hector's walking speed is approximately 4 km/h. Calculate the length of the path around the lake and how many hours Mr. Hector would have to walk to - Nozzle water speed
A water spray nozzle with a cross-section of 1.5 cm² sprays water at a speed of 24 m/s. What is the speed of the current in the supply pipe whose cross-section has a volume of 18 cm²? - Dividing a Circle
Draw a circle k, r = 4 cm, and divide it into two parts in a ratio of 1:5. - Republic
First, guess which circle has the larger diameter: the one with the same area as the area of the Czech Republic, or the one with a circumference equal to the length of the border of the Czech Republic? Then check your guess by calculating. The area of the - MO circles
George built the ABCD square with a 12 cm side. In this square, he scattered a quarter circle with a center at point B passing through point A and a semicircle l with a center at the center of the BC side and passed point B. He would still build a circle - 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.) - Clock angle
Calculate the magnitude of the angle formed by the lines p and q, which connect 1, 6 (line p), and 5, 8 (line q) on the clock face. - Wiring
A conduit has a cross-section of 54 mm². Is it possible to fit 6 conductors each with a cross-section of 6.7 mm² inside it? - Calculate 449
Calculate the size of the angle formed on a clock face by the lines connecting the centre to the positions at 7:12 and 1:24. - Parallels and one secant
There are two different parallel lines, a, b, and line c, that intersect the two parallel lines. Draw a circle that touches all lines at the same time. - Circle
The circle touches two parallel lines, p, and q, and its center lies on line a, which is the secant of lines p and q. Write the equation of the circle and determine the coordinates of the center and radius. p: x-10 = 0 q: -x-19 = 0 a: 9x-4y+5 = 0 - Pizza Plate Minimum Diameter
A pizza in the shape of a circle occupies an area of 94.985 square cm. What is the smallest integer diameter in centimeters that the plate on which we want to place this pizza must have so that the plates do not overlap
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