this post was submitted on 07 Oct 2024
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Someone may want to double-check my math on this one, but the length of the sides will be dependant on the radius of the smaller circle
I look at your diagram and see:
And
I solved those (using substitution, then the quadratic formula) and got
Whether or not a negative length is meaningful in this context is an exercise left to the reader
Giving (for L=5.44):
I'm surprised that it solved to a single number, maybe I made a mistake.
That lines up pretty similarly with what I found also. The angle should be a constant since there is only one angle where the relationship would be true. I just left it in terms of π because I try to avoid rounding.
Having said that, L would be a ratio of r; which I think lines up with what you found as well.