Circle - high school - examples
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.
- Circle chord
What is the length d of the chord circle of diameter 36 m, if distance from the center circle is 16 m?
The rectangle is 11 cm long and 45 cm wide. Determine the radius of the circle circumscribing rectangle.
How many times a day hands on a clock overlap?
- Cone A2V
Surface of cone in the plane is a circular arc with central angle of 126° and area 415 cm2. Calculate the volume of a cone.
- Square and circles
Square with sides 61 mm is circumscribed and inscribed with circles. Determine the radiuses of both circles.
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?
The areas of the two circles are in the ratio 2:20. The larger circle has diameter 20. Calculate the radius of the smaller circle.
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?
- Circle arc
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.
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.
Two gears, fit into each other, has transfer 2:3. Centres of gears are spaced 82 cm. What are the radii of the gears?
- Rhombus and inscribed circle
It is given a rhombus with side a = 75 cm and the radius of the inscribed circle r = 36 cm. Calculate the length of its two diagonals.
Convert 270° to radians. Write result as multiple of number π.
To circle with a radius of 41 cm from the point R guided two tangents. The distance of both points of contact is 16 cm. Calculate the distance from point R and circle centre.
- Circular pool
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?
Calculate perimeter of the circle described by a triangle with sides 478, 255, 352.
- Arc and segment
Calculate the length of circular arc l, area of the circular arc S1 and area of circular segment S2. Radius of the circle is 33 and corresponding angle is ?.
- Plastic pipe
Calculate weight of the plastic pipe with diameter d = 70 mm and length 380 cm if the wall thickness is 4 mm and the density of plastic is 1367 kg/m3.
Cylinder shell has the same content as one of its base. Cylinder height is 15 dm. What is the radius of the base of the cylinder?