>A 180° arc cannot straddle a 180° gap This can be the case if the other point is exactly 180 degrees from the anchor point that works though? But I think this

>A 180° arc cannot straddle a 180° gap This can be the case if the other point is exactly 180 degrees from the anchor point that works though? But I think this case occurs with probability 0 ("almost never") so can basically be ignored. Also the "obvious (wrong) answer" that reasons "by symmetry" is interesting since the n=3 case _can_ actually be solved in this manner. It's well known that probability the center of the circle is contained in the triangle of 3 randomly chosen points can be computed is 1/4. (This can be found by placing 1 point arbitrarily then computing an integral that ranges over the arc length to the second point). For the n=4 case this can be done via a double integral considering two arcs but it's slightly more annoying. I think there was a 3b1b problem about this that presents the more elegant approach the other commenter mentions.