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November 17th, 2013, 03:29 AM  #1 
Senior Member Joined: Apr 2012 Posts: 799 Thanks: 1  the radius of the small circle O_2
[attachment=0:vo8hqsqd]radius of the small circle.jpg[/attachment:vo8hqsqd]

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 ( ) 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 passes through . Therefore, (36r)^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  
Senior Member Joined: Jul 2013 From: Croatia Posts: 180 Thanks: 11  Re: the radius of the small circle O_2 Quote:
 
November 17th, 2013, 09:28 AM  #5  
Senior Member Joined: Nov 2013 From: Baku Posts: 502 Thanks: 56 Math Focus: Geometry  Re: the radius of the small circle O_2 Quote:
 
November 17th, 2013, 12:59 PM  #6  
Senior Member Joined: Jul 2013 From: Croatia Posts: 180 Thanks: 11  Re: the radius of the small circle O_2 Quote:
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: 20,746 Thanks: 2133 
The small circle's radius is exactly 6.

November 18th, 2013, 05:45 AM  #8  
Senior Member Joined: Apr 2012 Posts: 799 Thanks: 1  the radius of the small circle Quote:
 
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  
Senior Member Joined: Apr 2012 Posts: 799 Thanks: 1  Re: the radius of the small circle O_2 Quote:
many thanks  

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