# Circle + right triangle - examples

- Circle described

The radius of the circle described to the right triangle with 6 cm long leg is 5 cm. Calculate the circumference of this triangle. - Waste

How many percents are waste from a circular plate with a radius of 1 m from which we cut a square with the highest area? - 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. - Cone A2V

Surface of cone in the plane is a circular arc with central angle of 126° and area 415 cm^{2}. 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. - 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? - 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. - Tangents

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? - Cap

Jesters hat is shaped a rotating cone. Calculate how much paper is needed to the cap 60 cm high when head circumference is 52 cm. - Equilateral triangle

How long should be the minimum radius of the circular plate to be cut equilateral triangle with side 7 mm from it? - Hexagon A

Calculate area of regular hexagon inscribed in circle with radius r=9 cm. - OK circle

Calculate the radius (circumradius) of the circle described right triangle with hypotenuse long 33 and one cathetus long 17. - n-gon II

What is the side length of the regular 5-gon circumscribed circle of radius 11 cm? - Circle section

Equilateral triangle with side 33 is inscribed circle section whose center is in one of the vertices of the triangle and the arc touches the opposite side. Calculate: a) the length of the arc b) the ratio betewwn the circumference to the circle sector. - Cut and cone

Calculate the volume of the rotation cone which lateral surface is circle arc with radius 15 cm and central angle 63 degrees. - The chord

Side of the triangle inscribed in a circle is a chord passing through circle center. What size are the internal angles of a triangle, if one of them is 40°? - n-gon

What is the side length of the regular 5-gon inscribed in a circle of radius 12 cm? - Track arc

Two straight tracks is in an angle 74°. They will join with circular arc with radius r=1127 m. How long will be arc connecting these lines (L)? How far is the center point of arc from track crossings (x)?

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