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Moderator Note: At the time that this question was posted, it was from an ongoing contest. The relevant deadline has now passed.

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

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    What do "$OA$", "$OB$" and "triangle $OAB$" mean when $O$ is a circle?2012-09-28
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    I guess $O$ is the center?2012-09-28
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    yes O is the center2012-09-28
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    Hint: Assumming $O$ is the center, and the points are _on_ the circle (not inside it!), see that the event of interest (intersection inside circle) depends on the angle between $OA$ and $OB$.2012-09-28
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    @MitTripathi: Circumcentre idea will work. One can use it (or other methods) to identify the angle mentioned in the answer by Brian M. Scott.2012-09-28
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    I'm voting to close this question as off-topic because it was asked while it was a question in an on-going contest.2015-03-17

2 Answers 2