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I think the circles are for when you create the arc using the compass. Presumably you already constructed points A and B and joined them into a segment, so the

• bee_rider 3y ago
  If you are just trying to show the relationship between the lines, I don’t think there’s any reason to set A and B beforehand. Of course, it could be the case that there’s a multi-step proof where you do care about the positions of A and B in relation to some other things. But I think that would require doing the analysis with that in mind. Maybe the order in which you construct the more complicated proof can also benefit from picking certain points to be exact.