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 \(n\).

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