Externally Tangential

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 $k^2$ ?