You need to sit down and think about what you need to do. So far, you have stated only a very amorphous set of specs for your job/homework/project.
Define what the real problem is, in terms of mathematics. Is your problem solvable at all? So far, for example, the distance between two tangent lines is almost always zero. So your question makes no sense at all.
Once you have done that, then you can try to turn it into computer code.
