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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? – Sidd Singal Nov 13 '12 at 22:14
  • 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) – Eric Angle Nov 13 '12 at 22:16
  • Do you mean three points in (interior, or interior and perimeter) the circle, or on the circle (vs. in the interior of the circle)? – amWhy Nov 13 '12 at 22:26
  • I mean ON the circle – Xxx Nov 13 '12 at 22:38
  • as pointed out by Eric, you need to specify what you mean by random – picakhu Nov 13 '12 at 22:45
  • @Eric: The analogy to the Bertrand paradox isn't quite fitting -- in fact the Wikipedia article you linked to 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. – joriki Nov 13 '12 at 23:13
  • @picakhu uniform distibution – Xxx Nov 14 '12 at 11:24

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