2020 AMC 12A Problem 24

Suppose that $\triangle ABC$ is an equilateral triangle of side length $s$ , with the property that there is a unique point $P$ inside the triangle such that $AP = 1$ , $BP = \sqrt{3}$ , and $CP = 2$ . What is $s?$

$\textbf{(A) } 1 + \sqrt{2} \qquad \textbf{(B) } \sqrt{7} \qquad \textbf{(C) } \frac{8}{3} \qquad \textbf{(D) } \sqrt{5 + \sqrt{5}} \qquad \textbf{(E) } 2\sqrt{2}$

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.