Two circles, and , lie in the same plane.

The center of circle lies on circle .

Condition :

If the center of circle B lies on circle A.

Now draw all the possibilities.

Figure 1 :

Figure 2 :

Figure 3 :

Now from the figure 3 If the center of circle lies on circle , then circle and circle intersect at points.

Therefore, the correct choice is .

The correct choice is .