A circle \( x^{2}+y^{2}+4 x-2 \sqrt{2} y+c=0 \) is the director cir...

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A circle \( x^{2}+y^{2}+4 x-2 \sqrt{2} y+c=0 \) is the director circle
\( \mathrm{P} \) of the circle \( C_{1} \) and \( C_{1} \) is the director circle of circle \( C_{2} \)

W and so on. If the sum of radii of all these circles is 2 and if \( c=\lambda \sqrt{2} \), then the value of \( \lambda \) is
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