Ratio of squares

A circle is given in which a square is inscribed. The smaller square is inscribed in a circular arc formed by the side of the square and the arc of the circle. What is the ratio of the areas of the large and small squares?

Correct result:

r =  0:0

Solution:

$$\begin{gathered} r_1=1 \\ u=2r_1=\sqrt{2}{a}_1 \\ {a}_1=2\cdot r_1\mathrm{/}\sqrt{2}=2\cdot 1\mathrm{/}\sqrt{2}=\sqrt{2}\doteq 1.4142 \\ {S}_1=a_1^2=1.4142^2=2 \\ {S}_2=a_2^2=0 \\ r=S_1\mathrm{/}{S}_2=2\mathrm{/}0\approx INF=0:0 \end{gathered}$$

Try another example

Showing 0 comments:

Next similar math problems:

• Arc and segment
  Calculate the length of circular arc l, area of the circular arc S₁ and area of circular segment S₂. Radius of the circle is 11 and corresponding angle is ?.
• Square and circles
  The square in the picture has a side length of a = 20 cm. Circular arcs have centers at the vertices of the square. Calculate the areas of the colored unit. Express area using side a.
• Silver medal
  To circular silver medal with a diameter of 10 cm is inscribed gold cross, which consists of five equal squares. What is the content area of silver part?
• Pentagon
  Calculate the length of side, circumference and area of a regular pentagon, which is inscribed in a circle with radius r = 6 cm.
• Circular segment
  Calculate the area S of the circular segment and the length of the circular arc l. The height of the circular segment is 2 cm and the angle α = 60°. Help formula: S = 1/2 r2. (Β-sinβ)
• Circle arc
  Circle segment has a circumference of 135.26 dm and 2096.58 dm² area. Calculate the radius of the circle and size of the central angle.
• Circles
  The areas of the two circles are in the ratio 2:20. The larger circle has a diameter 20. Calculate the radius of the smaller circle.
• Concentric circles
  There is given a circle K with a radius r = 8 cm. How large must a radius have a smaller concentric circle that divides the circle K into two parts with the same area?
• Squares ratio
  The first square has a side length of a = 6 cm. The second square has a circumference of 6 dm. Calculate the proportions of the perimeters and the proportions of the contents of these squares? (Write the ratio in the basic form). (Perimeter = 4 * a, conte
• Quarter circle
  What is the radius of a circle inscribed in the quarter circle with a radius of 100 cm?
• Equilateral triangle vs circle
  Find the area of an equilateral triangle inscribed in a circle of radius r = 9 cm. What percentage of the circle area does it occupy?
• Circle section
  Equilateral triangle with side 33 is inscribed circle section whose center is in one of the vertices of the triangle and the arc touches the opposite side. Calculate: a) the length of the arc b) the ratio betewwn the circumference to the circle sector and
• An equilateral
  An equilateral triangle is inscribed in a square of side 1 unit long so that it has one common vertex with the square. What is the area of the inscribed triangle?
• Cathethus and the inscribed circle
  In a right triangle is given one cathethus long 14 cm and the radius of the inscribed circle of 5 cm. Calculate the area of this right triangle.
• 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?
• 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.
• Folding table
  The folding kitchen table has a rectangular shape with an area of 168dm2 (side and is 14 dm long). If necessary, it can be enlarged by sliding two semi-circular plates (at sides b). How much percent will the table area increase? The result round to one-hu