Externally Tangential

Level pending

Given the two sets on the xy-plane \[A=\left\{ (x,y) \mid x^2+y^2=100 \right\}, B=\left\{ (0,1), (k,2) \right\},\] \(2\) circles are represented by the set \[P=\left\{ (a_1+b_1, a_2+b_2) \mid (a_1, a_2) \in A, (b_1, b_2) \in B \right\}.\] If these \(2\) circles are externally tangential to each other, what is the value of \(k^2\)?

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