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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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Some Thoughts re(2): You're right! | Comment 47 of 51 |
(In reply to re: You're right! by Charlie)

Choosing two random points to form a chord is different from choosing a random chord though.

Imagine two chords, one if shorter than the other.  Then using the two-point method, the longer one has a higher chance than the shorter one, simply because the longer one cover more points.

However, the problem states that a random chord, implying each chord has the same probability being generated.

Your mid-point algorithm, on the other hand, will generate the desired result because every mid-point uniquely determines the chord itself, and each mid-point is uniformly generated.

Edited on October 26, 2004, 6:56 pm
  Posted by Bon on 2004-10-26 18:54:02

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