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Question Number 116669 by Eric002 last updated on 05/Oct/20

Commented by Eric002 last updated on 05/Oct/20

$d \overset{´}{e m o n t r e r} q u e l e s t r i a n g l e s A B C e t I J K$ $o n t l e m \hat{e m e} c e n t r e d e g r a v i t \overset{´}{e}$
	Answered by mindispower last updated on 05/Oct/20

	$s o i t G l e c e n t r d e A B C$ $e t G^{'} c e l u i d e K I J$ $d a n s t o u s c e q u i ? s u i t$ $A B = \vec{A B}$ $G A + G B + G C = 0 . . . 1$ $G^{'} K + G^{'} I + G^{'} J = 0 . . . 2$ $2 \Leftrightarrow$ $G^{'} A + A K + G^{'} B + B I + G^{'} C + C J = 0$ $1 \Leftrightarrow {G G}^{'} + G^{'} A + {G G}^{'} + G^{'} B + {G G}^{'} + G^{'} C = 0$ $\Leftrightarrow 3 {G G}^{'} + G^{'} A + G^{'} B + G^{'} C = 0$ $A K = C A, B I = A B, C J = B C$ $A K + B I + C J = A B + C J + B C$ $2 \Leftrightarrow G^{'} A + G^{'} B + G^{'} C + C A + A B + B C = 0$ $2 \Leftrightarrow G^{'} A + G^{'} B + G^{'} C = 0$ $2 \Leftrightarrow 3 {G G}^{'} = 0 \Rightarrow G = G^{'}$
	Commented by Eric002 last updated on 05/Oct/20

	$b r a v o p r o f e s s e u r$
	Commented by mindispower last updated on 06/Oct/20

	$j e v o u s e n p r i e$ $j e s u i s p a s p r o f e s s e u r j u s t$ $u n s i m p l e m a t h e u x$
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