Let r be the radius of the circle, then for the smaller square we can apply Pythagoras' Theorem:

$r^{2} = (\sqrt{x})^{2} + (\sqrt{x} / 2)^{2} = x + x / 4 = 5 x / 4$

and for the larger square:

$r^{2} = (\sqrt{y} / 2)^{2} + (\sqrt{y} / 2)^{2} = y / 2$

So x:y = 2:5.