Let \( A_{1}, A_{2}, A_{3}, \ldots, A_{n} \) are the vertices of a regular \( n \) sided polygon... VIDEO
Let \( A_{1}, A_{2}, A_{3}, \ldots, A_{n} \) are the vertices of a regular \( n \) sided polygon inscribed in a circle of radius \( R \). If \( \left(A_{1} A_{2}\right)^{2} \) \( +\left(A_{1} A_{3}\right)^{2}+\ldots+\left(A_{1} A_{n}\right)^{2}=14 R^{2} \), find the number of sides in the polygon.
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