# Find the polygon

Geometry Level 4

$\large \frac1{A_1 A_2} = \frac1{A_1 A_3} + \frac1{A_1 A_4 }$

If $$A_1, A_2, A_3, \ldots, A_n$$ are consecutive vertices of a regular $$n$$-sided polygon such that the equation above is fulfilled, find the value of $$n$$.

×