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Question Number 40960 by behi83417@gmail.com last updated on 30/Jul/18

Commented by MrW3 last updated on 30/Jul/18

$a \times \frac{b^{2} + c^{2} - a^{2}}{2 b c} + b \times \frac{a^{2} + c^{2} - b^{2}}{2 a c} = c \times \frac{a^{2} + b^{2} - c^{2}}{2 a b}$ $\times 2 a b c :$ $a^{2} (b^{2} + c^{2} - a^{2}) + b^{2} (a^{2} + c^{2} - b^{2}) = c^{2} (a^{2} + b^{2} - c^{2})$ $a^{2} b^{2} + a^{2} c^{2} - a^{4} + a^{2} b^{2} + b^{2} c^{2} - b^{4} = a^{2} c^{2} + b^{2} c^{2} - c^{4}$ $2 a^{2} b^{2} - a^{4} - b^{4} = - c^{4}$ ${(a^{2} - b^{2})}^{2} = c^{4}$ $\Rightarrow a^{2} - b^{2} = \pm c^{2}$ $\Rightarrow a^{2} = b^{2} + c^{2} o r b^{2} = a^{2} + c^{2}$ $\Rightarrow r i g h t a n g l e d t r i a n g l e i n b o t h c a s e s$
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