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Two-pipe Circumference Problem

Please see attached diagram.

I have an Engineering problem where straps are to be placed around two pipes. I know the diameter/radius of both pipes and the distance from centre to centre of both pipes. From this information, can I calculate the total strap length (this will be made up of two arc lengths around each pipe and two straight portions tangential to both pipes)?

I can draw it each time, but it would be useful to have an equation and having failed to work it out myself, I am now intrigued as to whether it can be done!

I looked at it as a problem of lots of right-angled triangles. I know I need to calculate the angle of the straight portions of the strap, but I lost my way a bit. Does anybody fancy having a go?!