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:

$$\begin{gathered} r=1 \\ {r}_2=r\mathrm{/}2=1\mathrm{/}2={\displaystyle \frac{1}{2}}=0.5 \\ u=2\cdot r_2=2\cdot 0.5=1 \\ a=u\mathrm{/}\sqrt{2}=1\mathrm{/}\sqrt{2}\doteq 0.7071 \\ S=a^2=0.7071^2={\displaystyle \frac{1}{2}}=0.5 \end{gathered}$$

Try another example

Showing 0 comments:

Next similar math problems:

• Quarter circle
  What is the radius of a circle inscribed in the quarter circle with a radius of 100 cm?
• Ratio of sides
  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.
• 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?
• Inscribed circle
  XYZ is right triangle with right angle at the vertex X that has inscribed circle with a radius 5 cm. Determine area of the triangle XYZ if XZ = 14 cm.
• ABCD square
  In the ABCD square, the X point lies on the diagonal AC. The length of the XC is three times the length of the AX segment. Point S is the center of the AB side. The length of the AB side is 1 cm. What is the length of the XS segment?
• 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.
• 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?
• Two annuluses
  The area of the annular circle formed by two circles with a common center is 100 cm². The radius of the outer circle is equal to twice the radius of the inner circle. Determine the outside circle radius in centimeters.
• Circles
  Area of circle inscribed in a square is 14. What is the area of a circle circumscribed around a square?
• Circular ring
  Square with area 16 centimeters square are inscribed circle k1 and described circle k2. Calculate the area of circular ring, which circles k1, k2 form.
• 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?
• 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.
• Five circles
  On the line segment CD = 6 there are 5 circles with radius one at regular intervals. Find the lengths of the lines AD, AF, AG, BD, and CE
• Concentric circles and chord
  In a circle with a diameter d = 10 cm, a chord with a length of 6 cm is constructed. What radius have the concentric circle while touch this chord?
• Equilateral triangle ABC
  In the equilateral triangle ABC, K is the center of the AB side, the L point lies on one-third of the BC side near the point C, and the point M lies in the one-third of the side of the AC side closer to the point A. Find what part of the ABC triangle cont
• 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?
• Chord
  It is given to a circle k(r=6 cm) and the points A, B such that / AB / = 8 cm lies on k. Calculate the distance of the center of circle S to the midpoint C of the segment AB.