Circle and chord

Geometry Level 4

If the values of \(a\) for which the common chord of circles \(x^2+y^2=8\) and \((x-a)^2+y^2=8\) subtends right angle at the origin are \(a_{1},a_{2},\ldots ,a_{n},\) then find \(n+\displaystyle \sum^{n}_{j=1}a_{j}+\displaystyle \prod^{n}_{j=1}a_{j}\).

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