Article with ID 26558 in ArcGIS Resource Center has described the steps. Here is an improved version:
1. Add the Advanced Editing toolbar to ArcMap by clicking View > Toolbars > Advanced Editing.
2. If Drawing toolbar does not appear, click on the Editor menu and select Start Editing.
3. Zoom in to the right position and size in order to make precise pinpoint of the circle of the circle, in following steps.
4. Click on the Marker tool (a little dot) on the Drawing toolbar.
5. Click somewhere on the map to specify where the center of the circle will be to place the Marker. Make an adjustment to the size of this Marker.
6. Click on the Circle tool on the Drawing toolbar.
7. Click the Markers on the map which specifies where the center of the circle will be, and don't release the button on your mouse.
8. Move your mouse little bit while still hold your mouse button, hit the 'R' key on the keyboard.
9. Specify the radius of the circle in map units and hit the Enter key.
10. If you do not want the Marker to be seen, you can either remove it or color it into invisible. The latter is suggested because any future move and copy may rely on this Marker to be precised.
Done.
To move or copy a circle, you may regard the center of the circle as base point. In this case, use the Marker as mentioned above.
1. Zoom in to the right position and size in order to make precise pinpoint for both old and new position of the center of the circle.
2. Click "Select Elements" button, then click the circle.
3. Press Ctrl in keyboard while click the Marker at the center of the circle, to grouping it.
4. Ctrl C and Ctrl V to copy and paste. For move, just use your mouse to drag and drop.
5. Drag and drop to right position base on the Marker.
http://resources.arcgis.com/content/kbase?fa=articleShow&d=26558
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