(((b+c)^2 )/(bc))l_a ^2 +(((a+b)^2 )/(ab))l_c ^2 +(((a+c)^2 )/(ac))l_b ^2 =(a+b+c)^2 l_b ,l_a ,l


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Question Number 148932 by vvvv last updated on 01/Aug/21

$\frac{{(b + c)}^{2}}{b c} l_{a}^{2} + \frac{{(a + b)}^{2}}{a b} l_{c}^{2} + \frac{{(a + c)}^{2}}{a c} l_{b}^{2} = {(a + b + c)}^{2}$ $l_{b}, l_{a}, l_{c} - b i s s e k t e r i s s a$ $p r o v e$
	Answered by mr W last updated on 01/Aug/21

	$s = \frac{a + b + c}{2}$ $l_{a} = \frac{2}{b + c} \sqrt{b c s (s - a)}$ $\frac{{(b + c)}^{2}}{b c} l_{a}^{2} = \frac{{(b + c)}^{2}}{b c} \times \frac{4 b c s (s - a)}{{(b + c)}^{2}} = 4 s (s - a)$ $Σ \frac{{(b + c)}^{2}}{b c} l_{a}^{2} = 4 s (3 s - a - b - c) = 4 s^{2}$ $= {(a + b + c)}^{2}$
	Commented by vvvv last updated on 01/Aug/21

	$t h a n k y o u$
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