Consider the circles $C_1\equiv {x}^2 + y^2- 4 = 0 $, $C_2\equiv {x}^2 + y^2- 6x +8= 0 $,$C_3\equiv {x}^2 + y^2- 8x- 2y + 16 = 0 $. The number of common tangents that can be drawn to touch at least two of the circle is

The circles are C1: x^2 + y^2 = 4 (center (0,0), r=2), C2: (x-3)^2 + y^2 = 1 (center (3,0), r=1), and C3: (x-4)^2 + (y-1)^2 = 1 (center (4,1), r=1). By calculating the distances between centers and comparing them to the sum/difference of radii, one can determine the number of common tangents for each pair. C1 and C2 are externally tangent (3 common tangents), C2 and C3 are separate (4 common tangents), and C1 and C3 are separate (4 common tangents). The total number of unique common tangents is 8.