Filled With Circles

$tan(EYF)=4$ so $\angle EYF=75.96^\circ$ . $\angle EYA=\frac{1}{2}\angle EYF=37.98^\circ.$

So from $\triangle AYE$ we get the radius $R=2\times tan(37.98^\circ)=1.56.$ Using that, the fact that $EZ=8$ , and similarity of $\triangle ZGF$ and $\triangle ZEY$ we get $x=FG=GZ\times \frac{EY}{EZ}=(8-2R)\times \frac{1}{4}=1.219$ .

So when going from $A$ to $B$ , sizes were scaled down by the factor $\frac{1.219}{2}=0.696$

Taking $R$ and scaling it back by the same factor three times, we get the answer $r=R\times 0.696^3=0.354$ .