# Polygone identity

Let $A_1, A_2, ..., A_k, k\ge 3$ lies on circle $(O)$ such that $A_1A_2=A_2A_3=...=A_kA_1$ and let $P\in (O)$ such that $arc PA_1=m.arc PA_2$. Prove that:

$\displaystyle \frac{1}{PA_1^2}+\frac{1}{PA_2^2}+...+\frac{1}{PA_k^2}=\frac{k^2}{4R^2sin^2(m\pi)}$

Author: Van Khea

Generalization: Tintarn