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Geometry Level 5

Find the smallest positive integral value of \(a\) for which the line \(y+x=0\) bisects two chords drawn from a point \( \displaystyle\large ( \frac{1+\sqrt{2}a}{2} , \frac{1-\sqrt{2}a}{2} ) \) to the circle whose equation is \( \displaystyle\large x^{2}+y^{2}-(\frac{1+\sqrt{2}a}{2}) x-(\frac{1-\sqrt{2}a}{2})y=0 \)

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