I'm confused on my calculations on analytic geometry with probability. Things I learned on these were messed up since I was a newbie on these subjects. Here's my problem:

Three points are chosen uniformly at random from the perimeter of circle. The probability that the triangle formed by these is acute can be expressed as $a/b$ where $a$ and $b$ are coprime positive integers. What is the value of $a+b$?

You may provide explanations so I would know how it was solved. Thank you


marked as duplicate by Adriano, DonAntonio, Johannes Kloos, Norbert, Stefan4024 Nov 3 '13 at 9:24

This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.

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    $\begingroup$ I don't think this is an exact duplicate. The fact that the triangle is acute if and only if the center of the circle is in its interior is in itself a mathematical proposition that may be worthy of attention in this context. $\endgroup$ – Michael Hardy Nov 3 '13 at 3:10
  • $\begingroup$ I'm sorry and I don't know that the question has exact contents as the previous one. But thanks for informing me about this. $\endgroup$ – bryan Nov 3 '13 at 4:48
  • $\begingroup$ @MichaelHardy, I think that if this is not an exact duplicate it is the closest thing to it: anyone attempting to answer the current question should be, imo, aware of basic geometry facts, so the present question and the one Adriano mentions are one and the same. $\endgroup$ – DonAntonio Nov 3 '13 at 5:06
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    $\begingroup$ This is a problem posted on Brilliant, as is several of OP's questions. Bryan, you can view the solutions directly. $\endgroup$ – Calvin Lin Nov 3 '13 at 16:18