Two circles whose radii are equal to $4$ and $8$ intersects at right angles. The length of  their common chord is:-

Let

$A=\left\{(x, y) \in R \times R \mid 2 x^{2}+2 y^{2}-2 x-2 y=1\right\}$

$B=\left\{(x, y) \in R \times R \mid 4 x^{2}+4 y^{2}-16 y+7=0\right\} \text { and }$

$C=\left\{(x, y) \in R \times R \mid x^{2}+y^{2}-4 x-2 y+5 \leq r^{2}\right\}$

Then the minimum value of $|r|$ such that $A \cup B \subseteq C$ is equal to:

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$x^{2}+y^{2}-10 x-10 y+41=0$

$x^{2}+y^{2}-24 x-10 y+160=0$ is .........