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Rectangle and set of points 
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#1
Jan713, 08:36 AM

P: 138

I found one interesting example...
We have a rectangle ABCD with his perimeter o. Where is the set of points when their (for each point) sum of distance lines AB, BC, CD, DA is 2/3o ? I tried it, but geometric problems is quite hard for me and I don't know how do it. So, have you got any idea? 


#3
Jan713, 01:15 PM

P: 350

I think the problem is to identify the set of points X such that
[itex] d(X,AB)+d(X,BC)+d(X,CD)+d(X,DA)= \frac{2}{3}*\text{Perimeter of Rectangle ABCD}.[/itex] The distances on the left hand side are lengths of perpendiculars dropped from the point X to the corresponding line. For example, if X lies inside the interior, then the left hand side would equal (1/2) the perimeter. So the locus cannot include points inside the rectangle. Without doing an explicit calculation, I bet the answer is an octogon. 


#4
Jan713, 03:37 PM

P: 138

Rectangle and set of points
Sorry for my English... And Vargo, yes, I mean this, thanks for wrote it in better form :)



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