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February 23rd, 2013, 01:02 PM  #1 
Newbie Joined: Feb 2013 Posts: 1 Thanks: 0  interesting one
Two points were randomly thrown in the square. Let's consider the circle which has these two points as ends of some diameter. What is the probability this circle lies strictly inside the square ? 
February 23rd, 2013, 09:49 PM  #2  
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 14,312 Thanks: 1023  Re: interesting one Quote:
Code:   . . .   . . .   . . .   by using something simpler, like a 4by4 checkerboard square with it's 9 points inside? 2 of the 9 points are picked at random, distance between the 2 points being the diameter. Here we know that 5 diameter lengths are possible: 1, 2, sqrt(2), sqrt(5) and sqrt(. Solve that...then graduate...  

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