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1 Answer

+1 vote

1-1/sqrt(2)

See picture for details.
x- the required value
r- is the radius of sphere=1
it is obvious the distance AO=sqrt(2) as sides of the large square = r=1
AC=AO-r=sqrt(2)-1
AC=x*sqrt(2) => x=AC/sqrt(2)=(sqrt(2)-1)/sqrt(2)=1-1/sqrt(2)
x=1-1/sqrt(2)

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