In \triangle A B C, we have A B=1 and A C=2. Side \overline{B C} and the median from A to \overline{B C} have the same length. What is B C ?
Answer Choices
A. \dfrac{1+\sqrt{2}}{2}
B. \dfrac{1+\sqrt{3}}{2}
C. \sqrt{2}
D. \dfrac{3}{2}
E. \sqrt{3}