Average Distance Between Points On or In a Circle

I recently came across an interesting math problem on youtube (why youtube keeps showing me these when I’m watching cooking shows, I’ll never understand, but I digress).  What is the average distance between two random points on a circle?  This can also be expanded to ask what is the average distance between two random points inside a circle?  Now of course I’m not going to sit down and do lots of math to figure this out, but it is a kinda interesting problem for a monte carlo simulation.  So I dusted the python off and went to work.

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