The exact solution will depend on how the data is presented. For example, as I mentioned, there are several ways to specify a line.
Remember, two points are not enough; you need at least three points to specify a circle - the points can't be all on the same line.
For the specified case, if you have a single line and a point of intersection, plus one more point, you do NOT have enough information; I suggest you make the graph and see that there are many solutions. The case is similar if you have one line and its point of intersection, plus the tangent line; it seems you don't have enough information either. I think you need both tangent lines, and the point of intersection.
Difference in opinions hath cost many millions of lives: for instance, whether flesh be bread, or bread be flesh; whether whistling be a vice or a virtue; whether it be better to kiss a post, or throw it into the fire... (from Gulliver's Travels)
