11. Isabella drew two circles with radii of 2 and 3 on a piece of paper, and then drew the common tangents to these two circles, getting exactly $k$ tangents. Then $k$ has $(\quad)$ possible cases.
(A) 2
(B) 3
(C) 4
(D) 5
(E) 6
11. D.

When two circles are concentric, $k=0$; when two circles are internally tangent, $k=1$; when two circles intersect, $k=2$; when two circles are externally tangent, $k=3$; when two circles are separated, $k=4$. Therefore, there are 5 possible values.