Question 117
In a regular $n$-gon, all the diagonals are drawn, forming smaller regular $n$-gons inside. If the outer regular $n$-gon has side length $1$, show that the $k$th largest regular $n$-gon formed has side length
$$
\frac{\cos (k \pi / n)}{\cos (\pi / n)}
$$
(where the original regular $n$-gon is the 1st largest).
$$
\frac{\cos (k \pi / n)}{\cos (\pi / n)}
$$
(where the original regular $n$-gon is the 1st largest).