Suppose that \triangle A B C is an equilateral triangle of side length s, with the property that there is a unique point P inside the triangle such that A P=1, B P=\sqrt{3}, and C P=2. What is s ?
Answer Choices
A. 1+\sqrt{2}
B. \sqrt{7}
C. \dfrac{8}{3}
D. \sqrt{5+\sqrt{5}}
E. 2 \sqrt{2}