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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.

My Progress:

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.

Thanks