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:

$r=1 \ \\ r_{2}=r/2=1/2=\dfrac{ 1 }{ 2 }=0.5 \ \\ u=2 \cdot \ r_{2}=2 \cdot \ 0.5=1 \ \\ \ \\ a=u / \sqrt{ 2 }=1 / \sqrt{ 2 } \doteq 0.7071 \ \\ \ \\ S=a^2=0.7071^2=\dfrac{ 1 }{ 2 }=0.5$

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