4

Part of 1995 Flanders Math Olympiad

Problems(1)

Flanders 5 ('95)

Source:

Given a regular

n

-gon inscribed in a circle of radius 1, where

n > 3

G(n)

as the average length of the diagonals of this

n

-gon. Prove that if

n \rightarrow \infty, G(n) \rightarrow \frac{4}{\pi}

complex numbers