Question 24Suppose 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?$$1 + \sqrt{2}$$\sqrt{7}$$\dfrac{8}{3}$$\sqrt{5 + \sqrt{5}}$$2\sqrt{2}$