# Circle + square root - examples

1. Circle chord
What is the length d of the chord circle of diameter 36 m, if the distance from the center circle is 16 m?
2. Rectangle
The rectangle is 11 cm long and 45 cm wide. Determine the radius of the circle circumscribing rectangle.
3. Square and circles
Square with sides 83 cm is circumscribed and inscribed with circles. Determine the radiuses of both circles.
4. Circles
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.
5. Rhombus and inscribed circle
It is given a rhombus with side a = 6 cm and the radius of the inscribed circle r = 2 cm. Calculate the length of its two diagonals.
6. Cone
Circular cone of height 15 cm and volume 5699 cm3 is at one-third of the height (measured from the bottom) cut by a plane parallel to the base. Calculate the radius and circumference of the circular cut.
7. 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.
8. Pizza
Pizza with a diameter 50 cm have weight 559 g. What diameter will have a pizza weighing 855 g if it is make from the same cloth (same thickness....) and same decorated?
9. Gold wire
From one gram of gold was pulled wire 2.1 km length. What is it diameter if density of Au is ρ=19.5 g/cm3?
10. Rotary cone
Rotary cone whose height is equal to the circumference of the base, has a volume 229 cm3. Calculate the radius of the base circle and height of the cone.
11. Circles
Area of circle inscribed in a square is 14. What is the area of a circle circumscribed around a square?
12. Chord
In a circle with radius r=60 cm is chord 4× longer than its distance from the center. What is the length of the chord?
13. Arc
Calculate span of the arc, which is part of a circle with diameter d = 20 m and its height is 6 m.
14. Circle
On the circle k with diameter |MN| = 61 J lies point J. Line |MJ|=22. Calculate the length of a segment JN.
15. Chord AB
What is the length of the chord AB if its distance from the center S of the circle k(S, 92 cm) is 10 cm?
16. Circles 2
Calculate the area bounded by the circumscribed and inscribed circle in triangle with sides 12 cm, 14 cm, 18 cm.
17. Shape
Plane shape has a maximum area 677 mm2. Calculate its perimeter if perimeter is the smallest possible.
18. Concentric circles
In the circle with diameter 19 cm is constructed chord 9 cm long. Calculate the radius of a concentric circle that touches this chord.
19. Rectangle and circle
The rectangle ABCD has side lengths a = 40 mm and b = 30 mm and is circumscribed by a circle k. Calculate approximately how many cm is circle long.
20. Rectangle
The rectangle is 18 cm long and 10 cm wide. Determine the diameter of the circle circumscribed to rectangle.

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