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.

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