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 answer:

S =  0.866

Step-by-step explanation:

$$\begin{gathered} r=1 \\ \mathrm{\Delta }r-r-r \\ {S}_1={\displaystyle \frac{\sqrt{3}}{4}}\cdot r^2={\displaystyle \frac{\sqrt{3}}{4}}\cdot 1^2\doteq 0.433 \\ S=2\cdot S_1=2\cdot 0.433=0.866 \end{gathered}$$

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