ILL 1986 Problem 56

Let $A_1A_2A_3A_4A_5A_6$ be a hexagon inscribed into a circle with center $O$ . Consider the circular arc with endpoints $A_1,A_6$ not containing $A_2$ . For any point $M$ of that arc denote by $h_i$ the distance from $M$ to the line $A_iA_{i+1} \ (1 \leq i \leq 5)$ . Construct $M$ such that the sum $h_1 + \cdots + h_5$ is maximal.