then prove \frac{1}{a+b}+\frac{1}{b+c}+\frac{1}{c+a}+\frac{1}{2}\cdot\frac{abc}{ab+bc+ca}\ge \frac{5}{3}.$$
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are the altitudes of the acute triangle 
. On the outside of the triangle , were built the square 
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. Prove that the sum of the areas of the rectangles and is equal to the area of the square .
and 
are the altitudes of the acute triangle 
. On the outside of the triangle , were built the square 
and thre rectangles 
, 
, with 
and 
. Prove that the sum of the areas of the rectangles and is equal to the area of the square .This post has been edited 4 times. Last edited by parmenides51, Apr 3, 2021, 6:19 PM
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as desired.
