Say you have a square with a diagonal length of R. Say you also have a line passing through the center of the square that is at angle A from the x axis. You then find an intersection between the square’s edge and the line. If you want to find the distance between this point and the center of the square as a function of angle A, what would that function be?

I have been unable to find a good function. I believe it would be some sort of period hyperbola, but I have no idea how to generate that.