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

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 November 17th, 2013, 07:07 AM #2 Senior Member   Joined: Jul 2013 From: Croatia Posts: 180 Thanks: 11 Re: the radius of the small circle O_2 $a \sqrt {2}-a=r+r \sqrt{2}$ $r=\frac {\sqrt 2-1}{\sqrt 2+1} a =(3-2 \sqrt 2) a$ ( $r=\approx 6.18$) for a=36 EDIT: ignore it
 November 17th, 2013, 08:15 AM #3 Senior Member     Joined: Nov 2013 From: Baku Posts: 502 Thanks: 56 Math Focus: Geometry Re: the radius of the small circle O_2 The segment $|DO_1|$ passes through $O_2$ . Therefore, (36-r)^2 = (36+r)^2 + 36^2 - 2*36*(36+r)*sin(pi/4) PS: Is there problem with latex?
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 $|DO_1|$ passes through $O_2$ . Therefore,
I don't think it does. I think it would pass through O2 if point C was on side of a square DE.

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.

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.

 November 17th, 2013, 11:36 PM #7 Global Moderator   Joined: Dec 2006 Posts: 20,978 Thanks: 2229 The small circle's radius is exactly 6.
November 18th, 2013, 05:45 AM   #8
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the radius of the small circle

Quote:
 Originally Posted by skipjack The small circle's radius is exactly 6.
Yes, you got it

 November 18th, 2013, 06:57 AM #9 Newbie   Joined: Apr 2009 Posts: 3 Thanks: 0 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?
November 18th, 2013, 02:18 PM   #10
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Re: the radius of the small circle O_2

Quote:
 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?
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