Question 75
Let $P$ be a regular hexagon. For a point $A$ let $d_{1} \leq d_{2} \leq \ldots \leq d_{6}$ be the distances from $A$ to the six vertices of $P$, ordered by size. Find the locus of all points $A$ in the interior or on the boundary of $P$ such that
a) $d_{3}$ takes the smallest possible value.
b) $d_{4}$ takes the smallest possible value.
a) $d_{3}$ takes the smallest possible value.
b) $d_{4}$ takes the smallest possible value.