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November 17th, 2013, 10:09 AM  #1 
Senior Member Joined: Nov 2013 From: Baku Posts: 502 Thanks: 56 Math Focus: Geometry  Circle, Triangle, Symmetry
Please solve this problem for me?

November 17th, 2013, 10:11 AM  #2 
Senior Member Joined: Nov 2013 From: Baku Posts: 502 Thanks: 56 Math Focus: Geometry  Re: Circle, Triangle, Symmetry
Sorry for attachment. Here smaller one.

November 27th, 2013, 05:16 PM  #3 
Senior Member Joined: Nov 2013 From: Baku Posts: 502 Thanks: 56 Math Focus: Geometry  Re: Circle, Triangle, Symmetry
I solved this problem. I hope some one will solve this > viewtopic.php?f=13&t=44386 
November 29th, 2013, 11:29 PM  #4 
Global Moderator Joined: Dec 2006 Posts: 20,746 Thanks: 2133 
Can you post your proof?

December 2nd, 2013, 01:49 PM  #5 
Senior Member Joined: Nov 2013 From: Baku Posts: 502 Thanks: 56 Math Focus: Geometry  Re: Circle, Triangle, Symmetry
Sure. [attachment=0:1np88ziz]triangleproblem222.png[/attachment:1np88ziz] 
December 3rd, 2013, 12:43 AM  #6 
Global Moderator Joined: Dec 2006 Posts: 20,746 Thanks: 2133 
What does "From HCID'" mean in the last line of your proof?

December 5th, 2013, 07:42 AM  #7 
Senior Member Joined: Nov 2013 From: Baku Posts: 502 Thanks: 56 Math Focus: Geometry  Re: Circle, Triangle, Symmetry
The sum of angles CID' + ID'H + D'HC + HCI = 360 and we get alpha + beta + gamma + theta = 180 degrees. Therefore D'_1DD'_2 is triangle. 
December 5th, 2013, 10:05 AM  #8 
Global Moderator Joined: Dec 2006 Posts: 20,746 Thanks: 2133 
You hadn't found angles CID' and D'HC. What values did you use for them?

December 5th, 2013, 02:36 PM  #9 
Senior Member Joined: Nov 2013 From: Baku Posts: 502 Thanks: 56 Math Focus: Geometry  Re: Circle, Triangle, Symmetry
angles CID' and D'HC are 90theta and 90gamma resp.

December 5th, 2013, 03:12 PM  #10 
Global Moderator Joined: Dec 2006 Posts: 20,746 Thanks: 2133 
But as you seemed to find that HCI = 180  (? + ?), and that ID'H = ? + ? + ? + ?, adding up the angles of HCID' then gives (90  ?) + (? + ? + ? + ?) + (90  ?) + (180  (? + ?)), which is 360 anyway, without implying that ? + ? + ? + ? = 180. 

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