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        riddles >> medium >> Circles Sequence
        
(Message started by: Immanuel_Bonfils on Jun 29th, 2008, 11:41am)
Title: Circles Sequence
Post by Immanuel_Bonfils on Jun 29th, 2008, 11:41am
http://www.ocf.berkeley.edu/~wwu/YaBBImages/symbols/ca.gif  is a circle of radius http://www.ocf.berkeley.edu/~wwu/YaBBImages/symbols/a.gif, internally tangent to another circle http://www.ocf.berkeley.edu/~wwu/YaBBImages/symbols/cb.gif with radius http://www.ocf.berkeley.edu/~wwu/YaBBImages/symbols/b.gif> http://www.ocf.berkeley.edu/~wwu/YaBBImages/symbols/a.gif. Let http://www.ocf.berkeley.edu/~wwu/YaBBImages/symbols/cc.gif  be any circle in the area (crescent shaped) between http://www.ocf.berkeley.edu/~wwu/YaBBImages/symbols/ca.gif and http://www.ocf.berkeley.edu/~wwu/YaBBImages/symbols/cb.gif, tangent to both.
     a) Find the locus of http://www.ocf.berkeley.edu/~wwu/YaBBImages/symbols/cc.gif’s center.
     b)  If ro is the radius of http://www.ocf.berkeley.edu/~wwu/YaBBImages/symbols/cc.gifo, one of  the above http://www.ocf.berkeley.edu/~wwu/YaBBImages/symbols/cc.gifs, what is the sequence rj, such that, (besides to satisfy http://www.ocf.berkeley.edu/~wwu/YaBBImages/symbols/cc.gif’s conditions)  http://www.ocf.berkeley.edu/~wwu/YaBBImages/symbols/cc.gifj+1 is tangent to http://www.ocf.berkeley.edu/~wwu/YaBBImages/symbols/cc.gifj?
      c) For a given ro, what is the maximum rj ?


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