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.)
re(2): You're right! | Comment 40 of 51 |
(In reply to re: You're right! by Charlie)

In the case of the random chords being chosen by taking a random point within the circle and using that as the midpoint of the chord, the following program simulates that:

RANDOMIZE TIMER
critDist = SQR(3) / 2
FOR i = 1 TO 100000
  x = 2 * RND(1) - 1
  y = 2 * RND(1) - 1
  dist = SQR(x * x + y * y)
  IF dist < 1 THEN
 
    IF dist < critDist THEN hit = hit + 1
    ct = ct + 1
  END IF
NEXT
p = hit / ct
q = 1 - p
PRINT USING "####### "; hit; ct;
PRINT USING "#.##### "; p; SQR(ct * p * q) / ct

In this case the positive case is reported (prob of chord length greater than radius). It is reported as
58866 78570 0.74922 0.00155
with the first two numbers signifying 58866 hits out of 78570 tries (as in some cases the random points were not even in the circle and thus not counted). The probability does match the 3/4 you had specified in a prior post.
  Posted by Charlie on 2003-11-17 16:11:15

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 (2)
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