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November 17th, 2013, 10:09 AM   #1
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Circle, Triangle, Symmetry

Please solve this problem for me?
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November 17th, 2013, 10:11 AM   #2
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Re: Circle, Triangle, Symmetry

Sorry for attachment. Here smaller one.
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November 27th, 2013, 05:16 PM   #3
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Re: Circle, Triangle, Symmetry

I solved this problem. I hope some one will solve this --> viewtopic.php?f=13&t=44386
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November 29th, 2013, 11:29 PM   #4
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Can you post your proof?
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December 2nd, 2013, 01:49 PM   #5
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Re: Circle, Triangle, Symmetry

Sure.
[attachment=0:1np88ziz]triangleproblem222.png[/attachment:1np88ziz]
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December 3rd, 2013, 12:43 AM   #6
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What does "From HCID'" mean in the last line of your proof?
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December 5th, 2013, 07:42 AM   #7
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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.
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December 5th, 2013, 10:05 AM   #8
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You hadn't found angles CID' and D'HC. What values did you use for them?
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December 5th, 2013, 02:36 PM   #9
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Re: Circle, Triangle, Symmetry

angles CID' and D'HC are 90-theta and 90-gamma resp.
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December 5th, 2013, 03:12 PM   #10
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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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