Question 363031
{{{drawing(300,300,-10,10,-10,10,circle(2,2,0.2),circle(-2,-2,0.2),circle(0,0,0.2),blue(line(-(2+2sqrt(2)),-(2+2*sqrt(2)),2+2sqrt(2),2+2sqrt(2))),line(2+2*sqrt(2) ,2+2*sqrt(2),2+2*sqrt(2),-(2+2*sqrt(2))),line(2+2*sqrt(2),-(2+2*sqrt(2)),-(2+2*sqrt(2)),-(2+2*sqrt(2))),line(-(2+2*sqrt(2)),-(2+2*sqrt(2)),-(2+2*sqrt(2)),2+2*sqrt(2)),line(-(2+2*sqrt(2)),2+2*sqrt(2),2+2*sqrt(2),2+2*sqrt(2)),
green(line(0,0,2,0)),
green(line(2,0,2,2)),
green(line(2,2,2+2*sqrt(2),2)),
locate(3,2,R),
locate(0.5,2,R),
locate(1,0,X),
locate(2.2,1.5,X),
locate(-1,6,16),
circle(2,2,2*sqrt(2)),circle(-2,-2,2*sqrt(2)))}}}
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From the diagram,
{{{X+R=8}}}
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{{{X^2+X^2=R^2}}}
{{{2X^2=R^2}}}
{{{X=R/sqrt(2)}}}
{{{X=(sqrt(2)/2)R}}}
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{{{(sqrt(2)/2)R+R=8}}}
{{{R=8/(1+sqrt(2)/2)}}} 
{{{R=16/(2+sqrt(2))}}}
{{{highlight(R=8(2-sqrt(2)))}}} or approximately,
{{{R=4.69}}}