Step 1: Remember the formulas of the radius of the circumscibed circle and radius  of the inscribed circle.

          NOTE: Radius R of the circumscibed circle and radius r of the inscribed

          circle to the same isosceles triangle of base b and lateral side a are given by 

                   R = \frac{a^2}{\sqrt{4a^2 - b^2}}

                   r = \frac{b}{2} \sqrt{\frac{2a - b}{2a + b}}

Step 2: Substitute a by 2 b (given) in both formulas and simplify 

            NOTE: R = \frac{(2b)^2}{\sqrt{4(2b)^2 - (b)^2}}

                         R = \frac{4b^2}{\sqrt{15b^2}}

                         R = \frac{4b}{\sqrt{15}}


                   r = \frac{b}{2} \sqrt{\frac{2(2b) - b}{2(2b) + b}}

                   r = \frac{b}{2} \sqrt{\frac{3}{5}}

Step 3: Find the ratio of the two radiuses

              NOTE: \frac{Radius R of the circumscibed circle}{radius r of the inscribed circle}

                   = \frac{\frac{4b}{\sqrt{15}}}{\frac{b}{2} \sqrt{\frac{3}{5}}}  

                  = \frac{8}{3}