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:

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

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