Let be the vertices of an -sided regular polygon such that

MATHEMATICS · Subjective · A Level · Mathematics · Trigonometry · Trigonometry

Problem

Let

A_1,A_2,A_3,\dots,A_n

be the vertices of an

n

-sided regular polygon such that

\frac{1}{A_1A_2}=\frac{1}{A_1A_3}+\frac{1}{A_1A_4}

. Find

n

. Prove or disprove the converse of this result.