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Putnam 1955 A2

Session A

$A_{1} A_{2} \ldots A_{n}$ is a regular polygon inscribed in a circle of radius $r$ and center $O . P$ is a point on line $O A_{1}$ extended beyond $A_{1}$ . Show that $\prod_{i=1}^{n} \overline{P A}_{i}=\overline{O P}^{n}-r^{n}$

Dataset text PutnamGAP. Quoted with source.

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