A square region A B C D is externally tangent to the circle with equation x^{2}+y^{2}= 1 at the point (0,1) on the side C D. Vertices A and B are on the circle with equation x^{2}+y^{2}=4. What is the side length of this square?
Answer Choices
A. \dfrac{\sqrt{10}+5}{10}
B. \dfrac{2 \sqrt{5}}{5}
C. \dfrac{2 \sqrt{2}}{3}
D. \dfrac{2 \sqrt{19}-4}{5}
E. \dfrac{9-\sqrt{17}}{5}