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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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Solution I'm no mathemetician: | Comment 34 of 51 |
I don't know if this is the solution, but I did arrive at a different answer than everyone else. My approach was to take the chord of radius r, draw the two radii to the center of the circle, and then calculate the distance of the line segment bisecting the chord (found here using the same method as (1/2r)*√3 that a few people used. I then used that point of bisection and drew a circle of radius (1/2r)*√3 and calculated the probability of the arc falling in the central circle (where the chord taken at random would have to be greater than the radius) compared to the area of the whole circle. The pi*r²'s cancel and you are finally left with 3/4 or 75%.
  Posted by Benjamin J. Ladd on 2003-11-16 12:04:21
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