touching circles offset by the radius

[grokker]

If there are touching circles in a straight line on the x axis (offset on the x axis by the diameter) and I want to arrange another line of circles touching the first line of circles (offset on the x axis by the radius) what is the formula for the offset on the y axis? I did this graphically in sketchup (attachment below). If the radius is 1, the y offset is ~1.75 but I would like to know the formula for figuring this out as well as the exact amount.

 

[grokker]

I think I figured it out but would like confirmation.

 

[Cubist]

Your work is correct, but you didn't finish off:-

[math] a=\sqrt{ d^2-r^2 } [/math]
[math] =\sqrt{ (2r)^2-r^2 } [/math]
[math] =\sqrt{ 4r^2-r^2 } [/math]
[math] =\sqrt{ 3r^2 } [/math]
[math] =\sqrt{ 3 } \times r [/math]