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November 17th, 2013, 03:29 AM   #1
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the radius of the small circle O_2

[attachment=0:vo8hqsqd]radius of the small circle.jpg[/attachment:vo8hqsqd]
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November 17th, 2013, 07:07 AM   #2
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Re: the radius of the small circle O_2



( ) for a=36

EDIT: ignore it
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November 17th, 2013, 08:15 AM   #3
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Re: the radius of the small circle O_2

The segment passes through .
Therefore,

(36-r)^2 = (36+r)^2 + 36^2 - 2*36*(36+r)*sin(pi/4)

PS: Is there problem with latex?
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November 17th, 2013, 08:45 AM   #4
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Re: the radius of the small circle O_2

Quote:
Originally Posted by tahirimanov
The segment passes through .
Therefore,


I don't think it does. I think it would pass through O2 if point C was on side of a square DE.
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November 17th, 2013, 09:28 AM   #5
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Re: the radius of the small circle O_2

Quote:
Originally Posted by crom
I don't think it does. I think it would pass through O2 if point C was on side of a square DE.
You are wrong O_2 and B are on DO_1 and intersection of OC and DO_1 is O_2.
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November 17th, 2013, 12:59 PM   #6
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Re: the radius of the small circle O_2

Quote:
Originally Posted by tahirimanov
Quote:
Originally Posted by crom
I don't think it does. I think it would pass through O2 if point C was on side of a square DE.
You are wrong O_2 and B are on DO_1 and intersection of OC and DO_1 is O_2.
No. The picture can be confusing.
That would be true if the circle touched side DE of a square, but since it doesn't touch it, then points O_2 and B don't lie on DO_1. The circle touches the arc DO_1 in point C not the side of a square.

Notice that I also thought that and posted a solution but it's WRONG.
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November 17th, 2013, 11:36 PM   #7
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The small circle's radius is exactly 6.
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November 18th, 2013, 05:45 AM   #8
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the radius of the small circle

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The small circle's radius is exactly 6.
Yes, you got it
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November 18th, 2013, 06:57 AM   #9
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Re: the radius of the small circle O_2

The small radius is the side of the square or the big radius divided by 6. r=R/6. So in this case is r=6
Do you need any proof?
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November 18th, 2013, 02:18 PM   #10
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Re: the radius of the small circle O_2

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Originally Posted by ssantos
The small radius is the side of the square or the big radius divided by 6. r=R/6. So in this case is r=6
Do you need any proof?
yes, please
many thanks
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