The line Ax+By=C (with C nonzero) is tangent to some circle centered at the origin.
What is the radius of that circle in terms of A, B, and C?
What is the point of tangency in terms of A, B, and C?
(In reply to Alternate solution
Ah, very good, Jer. I had been wondering why Brian asked for the radius first and the point of tangency second. Maybe his solution was more like yours. Charlie and I determined the point of tangency first.