Question 79
Given is a regular polygon $A_1A_2...A_{2010}$ centered at $O$. On each of the segments $OA_k$, with $k = 1, 2, ..., 2010$, lies the point $B_k$ such that
$$
\frac{OB_k}{OA_k} = \frac{1}{k}.
$$
Determine the ratio between the area of the polygon $B_1B_2...B_{2010}$ and that of $A_1A_2...A_{2010}$.
$$
\frac{OB_k}{OA_k} = \frac{1}{k}.
$$
Determine the ratio between the area of the polygon $B_1B_2...B_{2010}$ and that of $A_1A_2...A_{2010}$.