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Hi everyone I found this interesting question; help is appreciated! :)
We put 15 points on a circle O equally spaced. We then select two points A and B randomly from the 15 points. Find the probability that the perpendicular bisectors of OA and OB intersect inside Circle O.
The fact that these are perpendicular bisectors makes me want to think of triangles. So we have a triangle OAB and we want perpendicular bisectors of OA and OB to intersect inside the circle. The intersection of perpendicular bisectors is I believe the circumcenter. So we want the circumcenter of triangle OAB to inside circle O. After this point I have no idea what to do.