Puzzle #1 – Crossed Drive Belt

Imagine two wheels, of radius r and R. Their centres are a distance D apart.

A drive belt is stretched over the two wheels in an unconventional (and, I must admit, impossible) fashion such that the drive belt stretches from the top of one wheel to the underside of the other wheel, round the back then back over and round to the other wheel  – just feast you eyes on this lovingly crafted diagram for details:

Crossed Drive Belt

Question: How long is the drive belt? And also, at what distance from the small circle’s centre (or large circle if you prefer) does the belt cross itself?

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