Problem 1517 (difficulty: 3/10)

Let \(\displaystyle A_1A_2\ldots A_n\) be the vertices of a regular \(\displaystyle n\)-gon, inscribed into a unit circle, and let \(\displaystyle P\) be another point on the circle. Prove that

\(\displaystyle PA_1\cdot PA_2\cdot\ldots\cdot PA_n\le 2.\)

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