Triangle - high school - practice problems - page 49 of 51
Number of problems found: 1009
- Subtended 83194
A circle k with a center at point S and a radius of 6 cm is given. Calculate the size of the central angle subtended by a chord 10 cm long. - Equation of the circle
Find the equation of the circle inscribed in the rhombus ABCD where A[1, -2], B[8, -3], and C[9, 4]. - Circles
In the circle with a radius, 7.5 cm is constructed of two parallel chords whose lengths are 9 cm and 12 cm. Calculate the distance of these chords (if there are two possible solutions, write both). - Tetrahedral pyramid
Calculate the regular tetrahedral pyramid's volume and surface if the area of the base is 20 cm² and the deviation angle of the side edges from the plane of the base is 60 degrees.
- Support colum
Calculate the support column's volume and surface, which is shaped as a vertical quadrangular prism whose base is a rhombus with diagonals u1 = 102 cm and u2 = 64 cm. Column height is 1. 5m. - 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? - Angle of two lines
There is a regular quadrangular pyramid ABCDV; | AB | = 4 cm; height v = 6 cm. Determine the angles of lines AD and BV. - Similar frustums
The upper and lower radii of a frustum of a right circular cone are 8 cm and 32 cm, respectively. If the altitude of the frustum is 10 cm, how far from the bottom base must a cutting plane be made to form two similar frustums? - Lunes of Hippocrates
Calculate the sum of the area of the so-called Hippocratic lunas, which were cut above the legs of a right triangle (a = 6cm, b = 8cm). Instructions: First, calculate the area of the semicircles above all sides of the ABC triangle. Compare the sum of the
- Annulus
Two concentric circles with radii 1 and 9 surround the annular circle. This ring is inscribed with n circles that do not overlap. Determine the highest possible value of n. - Irregular hexagon
There is an irregular hexagon whose sides are the same length. The opposite sides are parallel; their distance is 237, 195, and193. What is its area? - Tangent
What distance are the tangent t of the circle (S, 4 cm) and the chord of this circle, which is 6 cm long and parallel to the tangent t? - Spherical cap
The spherical cap has a base radius of 8 cm and a height of 5 cm. Calculate the radius of a sphere of which this spherical cap is cut. - Quadrilateral 82395
The points ABC lie on the circle k(S, r) such that the angle at B is obtuse. How large must the angle at vertex B of quadrilateral SCBA be so that this angle is three times greater than the interior angle ASC of the same quadrilateral?
- Quadrilateral pyramid
In a regular quadrilateral pyramid, the side edge is e = 7 dm, and the diagonal of the base is 50 cm. Calculate the pyramid shell area. - Medians in triangle
The median of the isosceles triangle has a length of 3 cm. Determine the size of its sides if its perimeter is 16 cm. - Quadrilateral 7583
For the sizes of the interior angles of the quadrilateral ABCD, the following applies: the angle alpha is 26° greater than the angle beta, twice the angle Beta is 5° less than the angle gamma, and the angle gamma is 36° greater than the angle delta. Deter - Tetrahedral pyramid
What is the surface of a regular tetrahedral (four-sided) pyramid if the base edge a=16 and height v=16? - Circle annulus
There are two concentric circles in the figure. The chord of the larger circle, 10 cm long, is tangent to the smaller circle. What does annulus have?
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