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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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re(2): Different Approach (Continued) | Comment 25 of 51 |
(In reply to re: Different Approach (Continued) by Brian Smith)

It doesn't matter if you have 180 chords or 1800 chords, the number is still finite; we need to examine the entire infinite set of possible chords. As it turns out, as the number of chords approaches infinity, the probability approaches 2/3 (66.66...%).

The problem with this is assuming that the distribution of angles from a single point on the circumference is the same distribution of chords over the entire circle. In other words, you are assuming the same number of chords between 1° and 5° as between 76° and 80°, but how do you know that this is true for the entire infinite set of possible chords.
As Aaron pointed out, the chords closer to 0° and 180° are 'scrunched' together, while the chords around 90° are more spread out. That would seem to imply a different distrubution to accurately represent the entire range of possible chords.
  Posted by DJ on 2003-10-15 12:17:35

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