TMUA 2019 · Paper 1 · Question 6

The circles with equations

(x + 4)^{2} + (y + 1)^{2} = 64 and

(x - 8)^{2} + (y - 4)^{2} = r^{2} where r > 0

have exactly one point in common.

Find the difference between the two possible values of $r$ .