Inscribed triangle

Given a triangle ABC (any, but why not with sides 3,4,5, just as example),
construct the smallest similar triangle inscribed in ABC, that is with one vertex on each side.
It is not given which vertex of A'B'C' is on which side of ABC : find it for really smallest A'B'C' !
Calculate the sides of this smallest triangle. Solution

Details (includes applet, please wait..)

 

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