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# Trigonometry beauty

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 $$\dfrac{1}{\csc^2 A + \csc^2 B + \csc^2 C}$$

Note by U Z
2 years, 10 months ago

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

- 2 years, 10 months ago