Two circles

Two circles with the same radius r = 1 are given. The center of the second circle lies on the circumference of the first. What is the area of a square inscribed in the intersection of given circles?

Correct result:

S =  0.5

Solution:

r=1 r2=r/2=1/2=12=0.5 u=2 r2=2 0.5=1  a=u/2=1/20.7071  S=a2=0.70712=12=0.5r=1 \ \\ r_{2}=r/2=1/2=\dfrac{ 1 }{ 2 }=0.5 \ \\ u=2 \cdot \ r_{2}=2 \cdot \ 0.5=1 \ \\ \ \\ a=u / \sqrt{ 2 }=1 / \sqrt{ 2 } \doteq 0.7071 \ \\ \ \\ S=a^2=0.7071^2=\dfrac{ 1 }{ 2 }=0.5



Our examples were largely sent or created by pupils and students themselves. Therefore, we would be pleased if you could send us any errors you found, spelling mistakes, or rephasing the example. Thank you!





Please write to us with your comment on the math problem or ask something. Thank you for helping each other - students, teachers, parents, and problem authors.

Showing 0 comments:
avatar




Tips to related online calculators
Pythagorean theorem is the base for the right triangle calculator.
See also our trigonometric triangle calculator.

 
We encourage you to watch this tutorial video on this math problem: video1   video2

Next similar math problems:

  • Sphere in cone
    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
    circle_inside_rhombus Find the equation of the circle inscribed in the rhombus ABCD where A[1, -2], B[8, -3] and C[9, 4].
  • Hexagonal pyramid
    hexa_pyramid Calculate the volume and surface area of a regular hexagonal pyramid with a base edge a = 30 m and a side edge b = 50 m.
  • Diagonal BD
    trapezium_right Find the length of the diagonal BD in a rectangular trapezoid ABCD with a right angle at vertex A when/AD / = 8,1 cm and the angle DBA is 42°
  • Quadrilateral oblique prism
    kosyHranol What is the volume of a quadrilateral oblique prism with base edges of length a = 1m, b = 1.1m, c = 1.2m, d = 0.7m, if a side edge of length h = 3.9m has a deviation from the base of 20° 35 ´ and the edges a, b form an angle of 50.5°.
  • The regular
    hranol3b The regular triangular prism has a base in the shape of an isosceles triangle with a base of 86 mm and 6.4 cm arms, the height of the prism is 24 cm. Calculate its volume.
  • The triangles
    triangle_rt_taznice The triangles ABC and A'B'C 'are similar with a similarity coefficient of 2. The angles of the triangle ABC are alpha = 35°, beta = 48°. Determine the magnitudes of all angles of triangle A'B'C '.
  • Chimney and tree
    shadow Calculate the height of the factory chimney, which casts a shadow 6.5 m long in the afternoon. At the same time, a 6 m high tree standing near it casts a shadow 25 dm long.
  • Similar triangles
    triangles_2 Triangle A'B'C 'is similar to triangle ABC, whose sides are 5 cm, 8 cm, and 7 cm long. What is the length of the sides of the triangle A'B'C ' if its circumference is 80 cm?
  • Distance of points
    jehlan_4b_obdelnik_1 A regular quadrilateral pyramid ABCDV is given, in which edge AB = a = 4 cm and height v = 8 cm. Let S be the center of the CV. Find the distance of points A and S.
  • Triangular prism
    prism3_1 The triangular prism has a base in the shape of a right triangle, the legs of which is 9 cm and 40 cm long. The height of the prism is 20 cm. What is its volume cm3? And the surface cm2?
  • Quadrilateral pyramid
    jehlan3 In a regular quadrilateral pyramid, the height is 6.5 cm and the angle between the base and the side wall is 42°. Calculate the surface area and volume of the body. Round calculations to 1 decimal place.
  • Inclined plane
    naklonena_rovina The body stays on an inclined plane and exerts a compressive force of 70N on it. Find the angle between the inclined plane and the horizontal if a gravitational force of 100N acts on the body.
  • Calculate 7
    trapezium3 Calculate the height of the trapezoid ABCD, where coordinates of vertices are: A[2, 1], B[8, 5], C[5, 5] and D[2, 3]
  • Height
    triangle_rt1 The content of the triangle is 35 cm2. The length of the base is 10 cm. Determine the length of the height on the base.
  • Hexagonal pyramid
    hexa_pyramid Find the area of a shell of the regular hexagonal pyramid, if you know that its base edge is 5 cm long and the height of this pyramid is 10 cm.
  • Similar triangles
    triangles_2 The triangles ABC and XYZ are similar. Find the missing lengths of the sides of the triangles. a) a = 5 cm b = 8 cm x = 7.5 cm z = 9 cm b) a = 9 cm c = 12 cm y = 10 cm z = 8 cm c) b = 4 cm c = 8 cm x = 4.5 cm z = 6 cm