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Probability distribution functions for the perimeter and space of triangle with fixed radius

You choose three points (distributed uniformly) on the circle randomly. They form a triangle. What are dustibution laws for perimeter and area of triangle?

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    What is the square of a triangle?2012-11-13
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    You mean perimeter and AREA of the resulting triangle? Also, there may be some issues related to how you generate the three points in the first place -- see: http://en.wikipedia.org/wiki/Bertrand_paradox_(probability)2012-11-13
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    Do you mean three points *in* (interior, or interior and perimeter) the circle, or *on* the circle (vs. in the interior of the circle)?2012-11-13
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    I mean ON the circle2012-11-13
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    as pointed out by Eric, you need to specify what you mean by random2012-11-13
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    @Eric: The analogy to the Bertrand paradox isn't quite fitting -- in fact [the Wikipedia article you linked to](http://en.wikipedia.org/wiki/Bertrand_paradox_%28probability%29) offers "random endpoints" as one of the clarifications of "random chord". I fully agree that for completeness the question should specify that the points are chosen on the circle with uniform distribution, but, unlike in the case of a random chord, there is no question in this case what the natural distribution that one would informally think of as "random" is.2012-11-13
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    @picakhu uniform distibution2012-11-14

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