(1) If two circles are inscribed, the length of the connecting line is 4- 1=3.

The figure obtained by moving the center e is a circle with O as the center and a radius of 3;

(2) If two circles are circumscribed, the length of the connecting line is 4+ 1=5.

Then the figure obtained by moving the center E is a circle with O as the center and a radius of 5.