Putnam 1991 A4

Does there exist an infinite sequence of closed discs $D_1, D_2, D_3, \dots$ in the plane, with centers $c_1, c_2, c_3, \dots$, respectively, such that

1. the $c_i$ have no limit point in the finite plane,

2. the sum of the areas of the $D_i$ is finite, and

3. every line in the plane intersects at least one of the $D_i$?