Eight semicircles line the inside of a square with side length 2 as shown. What is the radius of the circle tangent to all of these semicircles?
Answer Choices
A. \dfrac{1+\sqrt{2}}{4}
B. \dfrac{\sqrt{5}-1}{2}
C. \dfrac{\sqrt{3}+1}{4}
D. \dfrac{2 \sqrt{3}}{5}
E. \dfrac{\sqrt{5}}{3}