# Circle - problems

- Construct

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. - An equilateral

An equilateral triangle with a side 10 m represents a wooden platform standing in a lawn. A goat is tied to a corner with a 15 m rope. What is the maximum amount of grazing area available to the goat? - Distance problem

A=(x, x) B=(1,4) Distance AB=√5, find x; - Pavement

Calculate the length of the pavement that runs through a circular square with a diameter of 40 m if distance the pavement from the center is 15 m. - Quarter circle

What is the radius of a circle inscribed in the quarter circle with a radius of 100 cm? - Circle annulus

There are 2 concentric circles in the figure. Chord of larger circle 10 cm long is tangent to the smaller circle. What are does annulus have? - Hands

The clock shows 12 hours. After how many minutes will agle between hour and minute hand 90°? Consider the continuous movement of both hands hours. - Circle chord

What is the length d of the chord circle of diameter 36 m, if distance from the center circle is 16 m? - Rectangle

The rectangle is 11 cm long and 45 cm wide. Determine the radius of the circle circumscribing rectangle. - Clock

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 dm^{2}. Calculate the volume of a cone. - Washer

Washing machine drum wash at 54 RPM. Washing machine motor pulley has diameter 5 cm. What must be the diameter of the drum machine pulley when the motor is at 301 RPM? - Square and circles

Square with sides 61 mm is circumscribed and inscribed with circles. Determine the radiuses of both circles. - Rectangle

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? - Circles

The areas of the two circles are in the ratio 5:14. The larger circle has diameter 23. Calculate the radius of the smaller circle. - MO SK/CZ Z9–I–3

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. - Cylinders

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 m^{2}area. Calculate the radius of the circle and size of central angle. - Rhombus

It is given a rhombus of side length a = 29 cm. Touch points of inscribed circle divided his sides into sections a_{1}= 14 cm and a_{2}= 15 cm. Calculate the radius r of the circle and the length of the diagonals of the rhombus. - Gear

Two gears, fit into each other, has transfer 2:3. Centres of gears are spaced 82 cm. What are the radii of the gears?

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