Circle + triangle - math problems

Number of problems found: 189

Wheel gear
A drive wheel of radius 2 is connected to a drive wheel of radius 1 by a pulley of length 17. What is the distance between the wheel axles?
Length of the chord
Calculate the length of the chord in a circle with a radius of 25 cm with a central angle of 26°.
Metal balls
Four metal balls with a diameter of 5 cm are placed in a measuring cylinder with an inner diameter of 10 cm. What is the smallest water volume to be poured into the cylinder so that all balls are below the water level?
Woman's day
We can easily make a heart for mothers for Woman's day by drawing two semicircles to 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?
Metal washers
Metal washers with a diameter of 80 mm are cut from a strip of steel sheet with a width of 10 cm and a length of 2 m. Calculate the percentage of material waste if no material is lost when two adjacent circles meet.
Right triangle
A circle with a radius of 5 cm is described in a right triangle with a 6 cm leg. What is the height at the hypotenuse of this triangle?
Five circles
On the line segment CD = 6 there are 5 circles with a radius one at regular intervals. Find the lengths of the lines AD, AF, AG, BD, and CE.
9-gon pyramid
Calculate the volume and the surface of a nine-sided pyramid, the base of which can be inscribed with a circle with radius ρ = 7.2 cm and whose side edge s = 10.9 cm.
Maximum of volume
The shell of the cone is formed by winding a circular section with a radius of 1. For what central angle of a given circular section will the volume of the resulting cone be maximum?
Surface and volume
Find the surface and volume of the rotating cone if the circumference of its base is 62.8 m and the side is 25 m long.
Sphere parts, segment
A sphere with a diameter of 20.6 cm, the cut is a circle with a diameter of 16.2 cm. .What are the volume of the segment and the surface of the segment?
Trapezoid - construction
Construct a trapezoid KLMN, where: k = 9 cm, l = 4 cm, m = 5 cm and angle α = 45°
Inscribed and described circle
Find the radii of a circle inscribed and circumscribed by a regular pentagon whose side measures 3 cm.
Sphere in cone
A sphere is inscribed in the cone (the intersection of their boundaries consists of a circle and one point). The ratio of the surface of the ball and the contents of the base is 4: 3. A plane passing through the axis of a cone cuts the cone in an isoscele
Find the 13
Find the equation of the circle inscribed in the rhombus ABCD where A[1, -2], B[8, -3] and C[9, 4].
Pentadecagon
Calculate the content of a regular 15-sides polygon inscribed in a circle with radius r = 4. Express the result to two decimal places.
Dodecagon
Calculate the size of the smaller of the angles determined by lines A1 A4 and A2 A10 in the regular dodecagon A1A2A3. .. A12. Express the result in degrees.
Two chords
From the point on the circle with a diameter of 8 cm, two identical chords are led, which form an angle of 60°. Calculate the length of these chords.
Circle and square
An ABCD square with a side length of 100 mm is given. Calculate the radius of the circle that passes through the vertices B, C and the center of the side AD.
Two parallel chords
In a circle 70 cm in diameter, two parallel chords are drawn so that the center of the circle lies between the chords. Calculate the distance of these chords if one of them is 42 cm long and the second 56 cm.