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Subject: "Question on the CTK article Chain of Inscribed Circles"     Previous Topic | Next Topic
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jprice2
Member since Mar-6-08
 Mar-06-08, 08:10 AM (EST)
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"Question on the CTK article Chain of Inscribed Circles"
 
   Hi, I was trying to follow the proof of the first result in this article and i still don't get the final step which states "However, the circles in every inverse pair are homothetic with the center of homothety at the center of inversion. Whence, h_n/R_n = h'_n/R'_n = 2n." I don't see why this ratio is true due to homothety. i know the radii of the two circles are related by homthety but i don't see how the heights have the same ratio as the radii. Thanks for any insights.


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alexb
Charter Member
2198 posts		 Mar-06-08, 10:55 AM (EST)
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1. "RE: Question on the CTK article Chain of Inscribed Circles"
In response to message #0
 
   I have just upgraded that page to make the argument more transparent. You have to consider two pairs of similar triangles:


  1. those formed by the line of circle centers and there common tangent, and
  2. those formed by the line of centers and the horizontal axis.

Please check the page and let me know if that's not clear enough.


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Thank You!
guest
 Mar-06-08, 08:50 PM (EST)
 
2. "RE: Question on the CTK article Chain of Inscribed Circles"
In response to message #1
 
   Thank you so much for your fast response! I don't know why I didn't see that relationship since it is not a subtle one. i know enough math that I should have spotted a simple relationship like that lol. my only excuse is that i examined the proof late at night while working 3rd shift! Wow, the concept of inversion certainly obviates alot of hard work in discovering the result of this theorem--very nice.
BTW, This sight is wonderful! It is full of mathematical goodies and cool interactive examples!! I can't imagine how much time it took to create this site but it was definitely time WELL SPENT. Thanks again for the help.
--John Price


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