Polygon Problem

Geometry Level pending

If \(A_1,A_2,\dots,A_n\) are the vertives of an \(n\)-sided regular polygon such that
\[\frac{1}{A_1A_2}=\frac{1}{A_1A_3}+\frac{1}{A_1A_4},\]
then find the number of sides of the polygon.

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