Categorizing answers as "clearly not in the spirit of the puzzle" or as "troll" answers seems subjective, no matter how obvious the categorization may be to you. Votes help quantify users' subjective views. So, there is already a mechanism in place to help address this concern about answers.
However, consider that "troll" answers can be useful for exploring the boundaries of a puzzle. I see the value of having stock answers to stock puzzles, but some people are going to respond with "but what if you go about it this other way..." and come at a puzzle from a different direction. Those answers should be collected, too, if they are not useless noise.
If a puzzle is garnering a high number of "troll" answers, though, the asker should seriously consider if the question is stated imprecisely or ambiguously. For example, with your first example question, the asker didn't mention circle centers except in a comment. Maybe many people are already familiar with the "spirit of the puzzle", but you can't legitimately fault answers that don't take into account unspecified restrictions. Of course, voting on the question is a mechanism to help persuade askers to do a better job describing puzzles.
Having said that, the burden on askers to trollproof questions seems particularly high for puzzle questions. With your first example question again, maybe it was originally designed to be answered by the average nerdy tween, but "trolls" who know technical definitions of words such as "line" and are familiar with different topologies are not going to limit their answers unless explicitly restricted. Perhaps Puzzling.SE needs something akin to PCG's list of standard loopholes then.