RU-ALLRUSSIAN 1962 Problem 8

Given a fixed regular pentagon ABCDE with side 1. Let M be an arbitary point inside or on it. Let the distance from M to the closest vertex be $\mathbf{r}_1$ , to the next closest be $\mathbf{r}_2$ and so on, so that the distances from M to the five vertices satisfy $\mathbf{r}_1 \leq \mathbf{r}_2 \leq \mathbf{r}_3 \leq \mathbf{r}_4 \leq \mathbf{r}_5$ . Find (a) the locus of M which gives $\mathbf{r}_3$ the minimum possible value, and (b) the locus of M which gives $\mathbf{r}_3$ the maximum possible value.