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?

Correct answer:

r =  0.65

Step-by-step explanation:

a=1 r1=a/4=1/4=14=0.25 r2=r12+(ar+r1)2    r2=r12+(ar+r1)2 r2=0.252+(1r+0.25)2  2.5r=1.625  r=1320=0.65



We will be pleased if You send us any improvements to this math problem. Thank you!



avatar




Tips to related online calculators
Looking for help with calculating roots of a quadratic equation?
Do you have a linear equation or system of equations and looking for its solution? Or do you have a quadratic equation?
Pythagorean theorem is the base for the right triangle calculator.

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

Related math problems and questions:

  • Circle and square
    square_axes 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.
  • RT sides
    described_circle_right_triangle Find the sides of a rectangular triangle if legs a + b = 17cm and the radius of the written circle ρ = 2cm.
  • Math heart
    srdce_1 Stylized heart shape created from a square with side 5 cm and two semicircles over his sides. Calculate the content area and its circumference.
  • Chord
    chord In a circle with radius r=60 cm is chord 4× longer than its distance from the center. What is the length of the chord?
  • Quarter circle
    quarter_circle_1 What is the radius of a circle inscribed in the quarter circle with a radius of 100 cm?
  • Ratio of sides
    described_circle2 Calculate the area of a circle with the same circumference as the circumference of the rectangle inscribed with a circle with a radius of r 9 cm so that its sides are in ratio 2 to 7.
  • Circle chord
    circles_6 Calculate the length of the chord of the circle with radius r = 10 cm, length of which is equal to the distance from the center of the circle.
  • Squares above sides
    pataVysky Two squares are constructed on two sides of the ABC triangle. The square area above the BC side is 25 cm2. The height vc to the side AB is 3 cm long. The heel P of height vc divides the AB side in a 2: 1 ratio. The AC side is longer than the BC side. Calc
  • Circumscribed circle to square
    kruznice Find the length of a circle circumscribing a square of side 10 cm. Compare it to the perimeter of this square.
  • Truncated cone 6
    frustum-of-a-right-circular-cone Calculate the volume of the truncated cone whose bases consist of an inscribed circle and a circle circumscribed to the opposite sides of the cube with the edge length a=1.
  • Two circles
    intersect_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?
  • RT and circles
    r_triangle Solve right triangle if the radius of inscribed circle is r=9 and radius of circumscribed circle is R=23.
  • A mast
    stoziar_1 A mast 32 meters high was broken by the wind so that its top touches the ground 16 meters from the pole. The still standing part of the mast, the broken part and the ground form a rectangular triangle. At what height was the mast broken?
  • Surface area of the top
    cylinder_4 A cylinder is three times as high as it is wide. The length of the cylinder’s diagonal is 20 cm. Find the surface area of the top of the cylinder.
  • Find radius
    numbers_49 Find the radius of the circle using the Pythagorean theorem where a=9, b=r, c= 6+r
  • 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].
  • Integer sides
    rt_triangle_1 A right triangle with an integer length of two sides has one leg √11 long. How much is its longest side?