Try circles!

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 $\displaystyle\large x^{2}+y^{2}-(\frac{1+\sqrt{2}a}{2}) x-(\frac{1-\sqrt{2}a}{2})y=0$