Pythagorean theorem + circle - practice problems - page 6 of 12
Number of problems found: 228
- Flakes
A circle was inscribed in the square. We draw a semicircle above each side of the square as above the diameter. This resulted in four chips. Which is bigger: the area of the middle square or the area of the four chips? - The mast
A 40 m high mast is secured in half by eight ropes 25 m long. The ends of the ropes are equidistant from each other. Calculate this distance. - Circle section
An equilateral triangle with side 33 is an inscribed circle section whose center is in one of the triangle's vertices, and the arc touches the opposite side. Calculate: a) the length of the arc b) the ratio between the circumference to the circle sector a - Right-angled 64084
A right-angled triangle ABC with sides 5 cm and 12 cm is described by circle k. Calculate the length of circle k in centimeters. When calculating, use π = 3, 14 and round the result to tenths.
- Cross-section 42981
Is it possible to cut a beam with a square cross-section with a side length of 30 cm from a log with a diameter of 42 cm? Write the answer as follows: yes, because. ... no, because... - Silver medal
A circular silver medal with a diameter of 10 cm is an inscribed gold cross consisting of five equal squares. What is the area of the silver part? b) What is the area of the golden cross? - Rhombus
It is given a rhombus of side length a = 20 cm. Touchpoints of inscribed circle divided his sides into sections a1 = 13 cm and a2 = 7 cm. Calculate the radius r of the circle and the length of the diagonals of the rhombus. - The rectangle 5
The rectangle OABC has one vertex at O, the center of a circle, and a second vertex A is 2 cm from the edge of the circle, as shown. The vertex A is also a distance of 7 cm from C. The point B and C lie on the circumference of the circle. a. What is the r - Two chords
In a circle with a radius of 8.5 cm, two parallel chords are constructed, the lengths of which are 9 cm and 12 cm. Find the distance of the chords in a circle.
- Pentagon
Calculate the length of a regular pentagon's side, circumference, and area, inscribed in a circle with a radius r = 6 cm. - Calculate 70814
The length of the sides AB and AD of the rectangle ABCD are in the ratio 3: 4. A circle k with a diameter of 10 cm describes a rectangle. Calculate the side lengths of a given rectangle. - Ratio of squares
A circle is given in which a square is inscribed. The smaller square is inscribed in a circular arc formed by the square's side and the circle's arc. What is the ratio of the areas of the large and small squares? - Circumscribed 83152
Given is an isosceles triangle whose base is 8 cm, and the sides are 15 cm long. Calculate the area of the triangle and the radius of the inscribed and circumscribed circle. - Woman's day
We can easily make a heart for mothers for Woman's day by drawing two semicircles on the two upper sides of the square standing on their top. What is the radius of the circle circumscribed by this heart when the length of the side of the square is 1?
- Circumscribed 83363
Triangle ABC, with sides a = 15 cm, b = 17.4 cm, and c = 21.6 cm, is circumscribed by a circle. Calculate the area of the segments determined by the sides of the triangle. - Two parallel chords
In a circle 70 cm in diameter, two parallel chords are drawn so that the circle's center lies between the chords. Calculate the distance of these chords if one of them is 42 cm long and the second 56 cm. - Described circle to rectangle
The rectangle with sides of 6 cm and 4 cm was circumscribed circle. What part of the circle area determined by the circumscribed circle occupies a rectangle? Express in perctentages(%). - Track arc
Two straight tracks are at an angle 74°. They will join with a circular arc with a radius r=1127 m. How long will the arc be connecting these lines (L)? How far is the arc's center point from track crossings (x)? - Circumscribed 81759
In triangle ABC, we know a = 4 cm, b = 6 cm, γ = 60°. Calculate the area and radius of the inscribed and circumscribed circle.
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