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From: "samik " <das.samik@gmail.com>
Newsgroups: comp.soft-sys.matlab
Subject: Re: One interesting problem in geometry
Date: Tue, 3 May 2011 00:10:22 +0000 (UTC)
Organization: University of Arizona
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"Florin Neacsu" wrote in message <ipngan$qp2$1@fred.mathworks.com>...
> "samik " <das.samik@gmail.com> wrote in message <ipndih$g5n$1@fred.mathworks.com>...
> > Given the coordinates of the 3 vertices of any triangle. How can we inscribe an equilateral triangle inside that given triangle.  That means the vertices of the equilateral triangle will lie on the sides of the given triangle.Any one has any closed form solution to plot this equilateral triangle?
> 
> Hi,
> 
> The intersection of the three bisectors(I guess this is the word for the line separating an angle into two equal angles) have a common intersection point which is the center of a circle. If you consider the radius of that circle as S/p with S the surface of the triangle and p the semi-perimeter, the you obtain an circle "interior" to the triangle. Whitin this circle you can construct an equilateral triangle.
> 
> If you need functions to plot all this, I think you can find on fileexchange "geom2d".
> 
> Regards,
> Florin 

Hi Florin,

But that triangle will not necessarily have its vertices falling on the sides of the given triangle. It will be inscribed in the circles though. Hence this will not be the solution of the problem that I mentioned.

Samik