Circle + triangle - practice problems - page 7 of 16
Number of problems found: 319
- Inscribed circle
Calculate the magnitude of the BAC angle in triangle ABC if it is three times less than the angle BOC, where O is the center of the circle inscribed in triangle ABC. - A cylinder
A cylinder 108 cm high has a circumference of 24 cm. A string makes exactly six complete turns around the cylinder while its two ends touch the top and bottom. (forming a spiral around the cylinder). How long is the string in cm? - Ruler and compass
Use a ruler and compass to construct a triangle ABC with AB 5cm BAC 60° and ACB 45°. - Coat of arms
The class created its coat of arms, which had a shape composed of an isosceles trapezoid ABCD (shorter base is a = 4.5 cm long, longer 2a = 9 cm, trapezoid height 6 cm) and a semicircle with center S and diameter AB. Three identical isosceles triangles fo - 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? - 10-centimeter-high 7638
A block with a square base is inserted into a 10-centimeter-high cylinder in such a way that its base is inscribed in the base of the cylinder. The edge of the base of the block measures 4 cm. Both bodies have the same height. Calculate the difference bet - Inscribed 43991
An irregular convex octagon is inscribed in the circle. Its four adjacent sides have a length of 3, and the remaining four adjacent sides have a size of 2. What is the area of a given octagon? - Same area
There is a given triangle. Construct a square of the same area. - The diagram 2
The diagram shows a cone with a slant height of 10.5cm. If the curved surface area of the cone is 115.5 cm². Calculate to correct three significant figures: *Base Radius *Height *Volume of the cone - 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. - Draw triangle
Construct right triangle MNO with hypotenuse o = 5 cm and angle MNO = 37° - Belongs 8412
Given a circle k(O; 2.5 cm), a line p: /Op/=4 cm, a point T: T belongs to p and at the same time /OT/=4.5 cm. We must find all the circles that will touch the circle k and the line p at point T. - Calculate 5115
In the rotating cylinder, it is given: V = 120 cm3, v = 4 cm. Calculate r, S mantle. - Dodecagon
Find the area of a regular dodecagon (n=12) if the radius of the circumscribed circle is 5 cm. - Cone-shaped 44161
How many square meters of roofing is needed to cover the cone-shaped roof, if the perimeter of its base is 15.7m and a height of 30dm - Semicircle
The semicircle with center S and the diameter AB is constructed equilateral triangle SBC. What is the magnitude of the angle ∠SAC? - Square inscribed
Find the length of the side of the square ABCD, which is inscribed to a circle k with a radius of 10 cm. - Circumscribed 7290
Calculate the area of a regular hexagon if the radius of the circle circumscribed is 6.8 cm. - Inscribed 7018
The dragon has the shape of a regular hexagon inscribed in a circle with a radius of 20 cm. What is the area of the dragon? - Intersection 40981
The intersection of a plane is 2 cm from the sphere's center, and this sphere is a circle whose radius is 6 cm. Calculate the surface area and volume of the sphere.
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