Easy draw a circle, intersectwith only tricky bit is it may have two answers. I take you want a programming answer not a drafting answer.
Manually do you really need code ? Circle grip-edit erase all done.
Code wise 2 picks, pick line near rotation point this returns length and correct point, pick pline, draw a circle and use intersectwith rotate line ask is correct press enter else draw 2nd answer. little busy at moment Lee may beat me anyway.
Grr correct that is why the pick of the line near the rotation end of the line, saves extra picks just compare pick pt to the two ends and the shortest distance is the rotation pt.