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Home » Mathematics » High School Basics (Ages 12-16)
 
Problem: 2004 AMC 10 #23
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#H34N1
Birch & Swinnerton Dyer
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#1
Problem: 2004 AMC 10 #23
Image
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I lost. Why do I lose so much?
Latest stupid mistake(s): 2^4\neq 8.
More combo help please kkthx[url]. Epic fail.....

PostPosted: Thu Feb 01, 2007 9:30 am  Back to top 
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jli
Navier-Stokes Equations
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#2
Re: Problem: 2004 AMC 10 #23
#H34N1 wrote:
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solution
Let the radius of circle B be r and the intersection of B and C be E.

The radius of the large circle is 2.

AB=1+r and BE=r so AE=\sqrt{2r+1}.

BD=2-r so DE=\sqrt{4-4r} and AE=1+\sqrt{4-4r}.

\sqrt{2r+1}=1+2\sqrt{1-r}

Now solve for r

PostPosted: Fri Feb 02, 2007 12:06 pm  Back to top 
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patelparth
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#3
how do you solve for r with the radicals?

PostPosted: Thu Feb 07, 2008 1:47 pm  Back to top 
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SnipedYou
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#4
Square both sides enough times to eliminate it

\sqrt{2r + 1} = 1 + 2\sqrt{1 - r}
2r + 1 = 1 + 4\sqrt{1 - r} + 4 - 4r
6r - 4 = 4\sqrt{1 - r}
36r^{2} - 48r + 16 = 16 - 16r
36r^{2} - 32r = 0
4r(9r - 8) = 0
r = \frac{8}{9}

PostPosted: Thu Feb 07, 2008 2:07 pm  Back to top 
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brightzhu
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#5
Is there a way to do this using trig?

PostPosted: Sun Feb 01, 2009 7:53 am  Back to top 
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AIME15
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#6
If there's a simple solution without trig, why would you want to use it?
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PostPosted: Sun Feb 01, 2009 3:23 pm  Back to top 
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soltixnj
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#7
There might be a simple solution with trig, or he could be more trig-inclined.

PostPosted: Sun Feb 01, 2009 3:38 pm  Back to top 
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