Question 18
Let $S$ be a set of 2017 distinct points in the plane. Let $R$ be the radius of the smallest circle containing all points in $S$ on either the interior or boundary. Also, let $D$ be the longest distance between two of the points in $S$. Let $a, b$ be real numbers such that $a \leq \frac{D}{R} \leq b$ for all possible sets $S$, where $a$ is as large as possible and $b$ is as small as possible. Find the pair $(a, b)$.