# Probability of a triangle in a circle [duplicate]

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, Stefan4024Nov 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.

• 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. – Michael Hardy Nov 3 '13 at 3:10
• 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. – bryan Nov 3 '13 at 4:48
• @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. – DonAntonio Nov 3 '13 at 5:06
• This is a problem posted on Brilliant, as is several of OP's questions. Bryan, you can view the solutions directly. – Calvin Lin Nov 3 '13 at 16:18