Pythagorean theorem + circle - practice problems - page 5 of 12
Number of problems found: 228
- A goat
In the square garden of side (a), a goat is tied in the middle of one side. Calculate the length of the rope (r) so that the goat grazes exactly half the garden. If r = c * a, find the constant c. - 6 regular polygon
A regular six-sided polygon has a side 5 cm long. Calculate its area. Compare how many more cm² (square centimeters) has a circle inscribed the 6-gon. - Rectangle - parallelogram
A rectangle is circumscribed by a circle with a radius of 5 cm. The short side of the rectangle measures 6 cm. Calculate the perimeter of a parallelogram ABCD, whose vertices are the midpoints of the sides of the rectangle. - Round table
A round table with a diameter d = 105 cm is coated by a square tablecloth with a side length 121 cm. About how many cm is the higher center of the tablecloth than its corners?
- Circle inscribed
There is a triangle ABC and a circle inscribed in this triangle with a radius of 15. Point T is the point of contact of the inscribed circle with the side BC. What is the area of the triangle ABC if | BT | = 25 a | TC | = 26? - Diameter 5668
The span of the arc is 247 cm, and the height of the arc is 21.5 cm. What is the diameter of the circle? - Circumscribed 2671
The circle's radius circumscribed by the rectangle is 5 cm, and one side of the rectangle is 6 cm long. Calculate the length of the other side and the area of the rectangle. - V-belt
Calculate the length of the belt on pulleys with diameters of 105 mm and 393 mm at shaft distance 697 mm. - Sin cos tan
If cos y = 0.8, 0° ≤ y ≤ 90°, find the value of (4 tan y) / (cos y-sin y)
- Circle and square
An ABCD square with a side length of 100 mm is given. Calculate the circle’s radius that passes through vertices B, C, and the center of the side AD. - Equilateral triangle vs circle
Find the area of an equilateral triangle inscribed in a circle of radius r = 9 cm. What percentage of the circle area does it occupy? - 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. - Determine 6415
Determine the distance of two parallel chords of lengths of 7 cm and 11 cm in a circle with a radius of 7 cm. - Cross-section 4343
Premium quality olive oil is sold in a glass bottle with a square cross-section packed in a special cylinder tube. The square's perimeter that forms the bottle's cross-section is 28 cm. What is the radius of this tube?
- Wheel gear
A drive wheel of radius two is connected to a drive wheel of radius one by a pulley of length 17. What is the distance between the wheel axles? - Concentric circles and chord
In a circle with a diameter d = 10 cm, a chord with a length of 6 cm is constructed. What radius has the concentric circle while touching this chord? - Pendulum
Calculate the pendulum's length 2 cm lower in the lowest position than in the highest position. The circular arc length to be described when moving is 20cm. - Again saw
We have a sculpture beam from the tree trunk with a rectangular cross-section with dimensions 91 mm and 87 mm. What is the trunk's smallest diameter? - Chord
In a circle with a radius r=60 cm is the chord, 4× longer than its distance from the center. What is the length of the chord?
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