If there is a triangle ABC . A similar triangle DEF is inscribed in triangle ABC such that D , E and F are the interior points of the sides AC , AB and BC. Show the ratio of area of inscribed triangle to the triangle ABC is always greater than or equal to \( \dfrac{1}{\csc^2 A + \csc^2 B + \csc^2 C}\)

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TopNewestjust a side note : In LaTeX (in general notation), we don't use \cosec instead we use \csc as in \(\csc x\)

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