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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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A Different Approach on Chords | Comment 21 of 51 |
Start with circle with center C and chord AB where A and B are random points on a circle. Draw radii, R, from C to A and from C to B. Designate angle ACB as alpha. Bisect angle alpha with a line from C to D, the midpoint of AB. Therefore, Sin(alpha/2) = AD/AC = AD/R. Or, Rsin(alpha/2) = AD. Since AD = AB/2, we now have 2Rsin(alpha/2)= AB. So the question is how often does 2Rsin(alpah/2)exceed R. Space is short so I will continue on the following sheet.
  Posted by Gordon Steel on 2003-10-13 15:55:28
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