Math people, I could use your help

[lxskllr]

Is that true even if the lines are not tangent to the circle?

I'm gonna say no, but I'm not sure. When I get a bit of extra time, I'll play with it. It's an interesting problem. Pizza would probably know for sure. My math skills are fairly weak. I taught myself what I needed to know, and programmed my calculator so I wouldn't have to do stuff repetitively. That was almost 30 years ago, and I forgot how to do the stuff by hand :^D I also don't have a core understanding of geometry. I can dig up formulas and stuff, but I don't understand the "whys" at a base level.

 

[dank69]

No worries. After some testing it looks like my formulas in post 21 are working. In addition, I had to work out some logic to deal with the cases where the radius is small enough that the 45 degree line never intersects the circle at all. I have just got that part working now.

I bet it could all be simplified with some calculus which is where I think ioni is going, but I need some hand-holding with that stuff.