Question 1101875
Just in all variables:

R, radius of outer, larger circle
r, radius of inner, shaded circle


The larger circle would be TWICE the area of the shaded smaller circle.
{{{pi*R^2-pi*r^2=pi*r^2}}}
{{{pi*R^2=pi*r^2+pi*r^2}}}
{{{pi*R^2=2*pi*r^2}}}


{{{2r^2=R^2}}}

{{{r^2=(1/2)R^2}}}

{{{r=R/sqrt(2)}}} or  {{{highlight(r=(sqrt(2)/2)R)}}}


You can substitute for R to finish.