Forgive me for not explaining the formula properly at the start.
Lets start my explanation of it again: this time I'll swap the variable for the Known Radius to "K" for additional clarity.
Starting with 2D:
The formula simply calculates a geometric value. It calculates the distance between the lowest point of a vertical line ( "L" in green ) and the 6 o'clock quadrant of the Known Radius circle when the top of the green line "L" ends on the Known Radius circle. With the Known Radius circle value staying constant, as the green line moves further from the 6 o'clock quadrant point, the value or R increases, up until R = K.
Moving to 3D:
My previous image was trying to portray what the image below shows: the circle calculated, with radius "R", from the Known Radius circle "K" value and the line "L" length inputted into the formula.
Note: The dimensions are in millimetres, so the discrepancy of 0.0001mm can be ignored.
So I'm looking for a way to be able to have a lisp routine prompt the user to select the line "L", store it's length, store it's end point coordinates (which will always be the it's lowest point, co-planar with the 6 o'clock quadrant point of the Known Radius circle) and draw a circle with the calculated radius from the formula.
To say I'm lost with how to implement this in autolisp is a big understatement. Would anyone like to do it and be paid for their expertise?