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Strike a Chord (..Any Chord) (Posted on 2003-10-09) Difficulty: 4 of 5
What is the probability that a randomly drawn chord will be longer than the radius of the circle?

Prove it.

No Solution Yet Submitted by DJ    
Rating: 4.5263 (19 votes)

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Program: | Comment 41 of 51 |
I'll post the program (second method using one fixed point and one random point) as soon as I get it put on this computer. The results were surprising! The average of 4 trials at 10,000 iterations of random chords produced not 66.66% as expected, but...

...75.00125

Which would seem to show that the method used to arrive at 66% (namely the choosing of a second random point on a circle in relation to a fixed point) is faulty somehow (I take it that it's because the point spreads are different from a fixed point). But I'm altogether happy about that! If that is the case, and 75% can be reached by both methods, then this problem isn't a paradox and it does have a real solution regardless of the method taken. I'm pretty sure I was wrong when I wrote my first program and after I find the error, I'll go ahead and post both programs.

Now--I'm only wondering why your program gave you 66%?
  Posted by Benjamin J. Ladd on 2003-11-18 15:38:31
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