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Algebra Level 3

Consider the \(4\) distinct points \((a, \frac{1}{a}), (b, \frac{1}{b}), (c, \frac{1}{c}), (d, \frac{1}{d})\) lying on a circle, centered at the origin, of radius \(4\).

Find \(a\times b\times c\times d\).

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