All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars    
perplexus dot info

Home > Shapes > Geometry
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)

Comments: ( Back to comment list | You must be logged in to post comments.)
Solution Sez me ... | Comment 1 of 51
2/3.

To draw a chord with a pencil, you put the pencil point somewhere on the circle, then draw a line to any other point on the circle. Orient a polar coordinate system such that the origin is at the center of the circle and the first point of the chord is at zero degrees. Then the second point of the chord can be anywhere from 0 to 360 degrees, exclusive.

A chord exactly as long as the circle'd radius will intersect the circle at +/- 60 degrees. Chords with their second point within this sector will be shorter than the radius, while chords with their second point outside this sector will be longer than the radius. since the area outside the sector from -60 to +60 degrees is 2/3 of the circle, the odds are 2/3.
  Posted by Bryan on 2003-10-09 14:49:53

Please log in:
Login:
Password:
Remember me:
Sign up! | Forgot password


Search:
Search body:
Forums (0)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (7)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Chatterbox:
Copyright © 2002 - 2017 by Animus Pactum Consulting. All rights reserved. Privacy Information