Question 919772
{{{drawing(300,300,-10,10,-10,10,circle(0,0,10),line(0,0,0,-10),line(0,0,10,0),locate(2,-2.5,x),circle(4.142,-4.142,4.142),blue(line(0,0,7.071,-7.071)),green(line(0,-4.142,4.142,-4.142)),green(line(4.142,0,4.142,-4.142)))}}}
The radius of the larger circle is R.
The radius of the smaller circle is r. 
The length of the green lines is r. 
So from the center of the large circle to the center of the small circle is 
{{{r^2+r^2=x^2}}}
{{{x=sqrt(2)r}}}
From the center of the large circle to the edge of the large circle is,
{{{x+r=R}}}
{{{sqrt(2)r+r=R}}}
{{{highlight(r=R/(1+sqrt(2)))}}}
So then,
{{{r=10/(1+sqrt(2))}}}