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'Interior Squares' printed from https://nrich.maths.org/
Let $r$ be the radius of the circle, then for the smaller square we
can apply Pythagoras' Theorem:
$r^2=(\sqrt{x})^2+(\sqrt{x}/2)^2=x+x/4=5x/4$
and for the larger square:
$r^2=(\sqrt{y}/2)^2+(\sqrt{y}/2)^2=y/2$
So $x:y = 2:5$.