# Sides of polygon!

Geometry Level 3

Let $$A_1, A_2, A_3, \ldots , A_n$$ denote vertices of a regular $$n$$ sided polygon inscribed in a circle of radius $$R$$.

If $$(A_1 A_2)^2 + (A_1 A_3)^2 + \cdots + (A_1 A_n)^2 = 14R^2$$, find the number of sides of the polygon.

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