WL indeed handles the symbolic case for equilateral triangle very well.
From the video linked in the head post the symbolic value of the radius for an equilateral triangle is $\sqrt{3}-\sqrt{2}$ .
You can change a to {1,Sqrt[3]} to form a equilateral triangle and run the attached notebook. The radius is about 0.318.
Nice! I wonder, is there a symbolic expression for a general (not equilateral) triangle case?
Thanks Shenghui. I had actually tried that change but for some reason the code was not working for me. Possibly I missed an initialization snippet. Anyway, it's a nice problem and solution method.
Interesting work. I have a question. How do I use this to find, either exactly or approximately, the value of the radius for the original problem (that is, with the equilateral triangle).
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