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Equally Spaced (Posted on 2018-05-13) Difficulty: 4 of 5

  
Let rectangle ABCD have x-y coordinates: A(0,0), B(0,h), C(w,h), and D(w,0) where h and w are positve real numbers.

1) Does there exist a point P with x-y coordinates (-r,-s) where r and s are
     positive real numbers such that ∠BPA = ∠APC = ∠CPD ?

2) If the answer to question 1) is yes, then are there functions f and g
     such that

         h = f(r,s)   and   w = g(r,s) ?
  

No Solution Yet Submitted by Bractals    
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re(2): Possible solution Comment 3 of 3 |
(In reply to re: Possible solution by Bractals)

I'm not at home where I have this all graphed on GSP, but using w=1, h=.51, s=.85 and solving to get r=.6857487086 then using these in the triple equation gives


.2150539976=.2163789613=.2150539977

That middle term can be close to the others but I don't think it can be exact.  I'll try more ideas later.



  Posted by Jer on 2018-05-21 14:04:57
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