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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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answer a ? with a ? | Comment 7 of 51 |
What is the probability that a randomly drawn chord will be the exact same length as the radius of the circle?

That said, I think the answer that DJ is looking for is 2/3 as others have figured.

my way of explaining:

>6 equilateral triangles can fit inside a circle.
(a picture does help)

>Take any two of these triangles that are next to each other.

>The triangles share 2 points: the center of the circle and a point you can defined as the arbitrary starting point of the chord.

>The other two points of the triangles- the most distant points- define 1/3 the circumference of the circle.

>If a chord is drawn from the arbitrary starting point to a point within this area it will be shorter than the radius.

>You can see how this is true because the two sides of the triangles which are chords themselves are the same lenth as the radius.

>Therefore, a chord drawn from the starting point to the other 2/3rds of the circle will be longer than the radius.
  Posted by geoffrey on 2003-10-09 17:16:55
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