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December 15th, 2012, 01:48 AM  #1 
Newbie Joined: Dec 2012 Posts: 1 Thanks: 0  probability problem
The problem is such: There is a unit circle on the plane. 3 points are randomly chosen from this circle ("randomly" means uniform distribution over the circle). What is the probability that circumscribed circle of the triangle made of these 3 points lies entirely inside the unit circle? I tried to express circumcenter and circumradius via coordinates of 3 points. Also I found that condition circumcircle lies inside unit circle is equivalent to W+R<=1, where W is distance from center of circumscribed circle to the origin, R is radius of circumscribed circle. But the formulas are so strange that I can't imagine how should I find probability integrating over region W+R<=1. Help please. 

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