KVPY SA Exam 19-Nov-2017 Question Paper

Let n ≥ 4 be a positive integer and let ${\mathit{l}}_1,{\mathit{l}}_2,......,{\mathit{l}}_{\mathit{n}}$ be the lengths of the sides of arbitrary n – sided non-degenerate polygon P. Suppose
$\frac{{\mathit{l}}_1}{{\mathit{l}}_2}+\frac{{\mathit{l}}_2}{{\mathit{l}}_3}+...+\frac{{\mathit{l}}_{\mathit{n}-1}}{{\mathit{l}}_{\mathit{n}}}+\frac{{\mathit{l}}_{\mathit{n}}}{{\mathit{l}}_1}=\mathit{n}$
Consider the following statements:
I. The lengths of the sides of P are equal.
II. The angles of P are equal.
III. P is a regular polygon if it is cyclic.
Then