SE-SKOLORNAS 1964 Problem 4

Points $H_1, H_2, ... , H_n$ are arranged in the plane so that each distance $H_iH_j \le 1$ . The point $P$ is chosen to minimise $\max (PH_i)$ . Find the largest possible value of $\max (PH_i)$ for $n = 3$ . Find the best upper bound you can for $n = 4$ .