Illustrator: snapping circles together in an interlocking way

Question

I'm looking for a solution for a certain problem. I have two sets of vertically evenly-spaced circles with equal gaps between circles in each column. I would like to know a way to find a point to achieve a perfect snap of both columns, so that they form an "interlocking" pattern.

I have a feeling it has to do with tangents, but the best I can do is to run a script that builds tangents between two circles. I tried it and I can't see a way for it to be helpful. I also tried googling for a solution, but none of the keywords that I used yielded a helpful result.

I tried drawing an equidistant line between two vertical circles, snapping another circle (1) to the bottom circle (2), and rotating it (1) so that its centre snaps with said line, but it's far from elegant. The cursor floats and I can only get a snap if I do that 15 times, checking how far the center point is from the line.

Reference image attached (right element is snapped manually and not in a perfect way):

Many thanks!

Answer 1

Draw the circles one on top of each other then use the rotate tool (r. Yes rotate tool not selection tool), move the pivot to center of each successive circle and rotate.

Alternate approach use numeric input in linetool and draw a zig zag with length of 2 times radius (or sum of different radiuses). Then move circles to snap centers to zigzag corners.

If you have trouble figuring angle to use darw a circle at first position with double the radius and find intersection with horizontal line.

Thats mathematics for you.