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Photo
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Line through a circle


Best Answer BMAD, 07 July 2013 - 04:56 PM

Spoiler for another method

 

 

I have three possible and perfectly acceptable solutions to this question each depending on what assumptions in your model you choose to make.  Only two of the three possibilities have been correctly (at least according to my logic) found.

 

Joyandwarmfuzzies- 1/3

K-Man                    - 1/2

 

But there is still another possibility that I would like examined.

these are the solutions.  Well done everyone!

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11 replies to this topic

#1 BMAD

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Posted 03 July 2013 - 04:03 AM

There is a circle with a radius of 1 on the ground.  A straight line intersects the circle.  What is the probability that the length of the chord created by the intersection of the circle and the line is greater than or equal to sqrt(3)?


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#2 rlsrainbow

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Posted 03 July 2013 - 05:18 AM

0.5358984


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#3 k-man

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Posted 03 July 2013 - 03:29 PM

Spoiler for


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#4 Joyandwarmfuzzies

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Posted 03 July 2013 - 06:35 PM

Spoiler for


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#5 Joyandwarmfuzzies

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Posted 03 July 2013 - 10:06 PM

Spoiler for Oops changed my mind


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#6 k-man

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Posted 03 July 2013 - 10:40 PM

Spoiler for some elaboration on my previous answer

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#7 BobbyGo

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Posted 03 July 2013 - 10:49 PM

Spoiler for

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#8 Yoruichi-san

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Posted 03 July 2013 - 11:02 PM

Yeah, I agree with k-man that different methods of drawing give different answers, but overall I think I agree with JAWF on the answer...

 

Spoiler for Why...

Edited by Yoruichi-san, 03 July 2013 - 11:02 PM.

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#9 bonanova

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Posted 06 July 2013 - 07:52 PM

The probability can reasonably vary by a factor of two,
depending on the description of "randomness" for the line.

There is a strong argument for "best" implementation of
randomness. It leads to one of the answers given above.
an answer not given above.

The reason it's best is that it gives the same result with circles
of any radius, and arbitrary center locations. It also has a
physical implementation that is satisfyingly random in nature.

What is it?

Edited by bonanova, 07 July 2013 - 07:32 AM.
Correction.

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#10 BMAD

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Posted 06 July 2013 - 08:55 PM

I have three possible and perfectly acceptable solutions to this question each depending on what assumptions in your model you choose to make.  Only two of the three possibilities have been correctly (at least according to my logic) found.

 

Joyandwarmfuzzies- 1/3

K-Man                    - 1/2

 

But there is still another possibility that I would like examined.


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