M a inside poin in ΔABC. M = bar {(A, area(MBC)), (B, area(MAC)),(C,area(MAB))}


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Question Number 194821 by sniper237 last updated on 16/Jul/23

$M a i n s i d e p o i n i n Δ A B C .$ $M = b a r {(A, a r e a (M B C)), (B, a r e a (M A C)), (C, a r e a (M A B))}$
Commented by mr W last updated on 16/Jul/23

$w h a t d o m e a n w i t h (A, a r e a (M B C)) ?$ $w h a t d o m e a n w i t h b a r {X, Y, Z} ?$
Commented by sniper237 last updated on 16/Jul/23
$barycentric sysrem of weighed poins G=bary{(A,a) , (B,b) ,(C,c)} ⇔ aGA^→ +bGB^→ +cGC^→ =0^→ IA^→ +IB^→ =0^→ ⇔ I=bary{(A,1),(B,1)}$
$b a r y c e n t r i c s y s r e m o f w e i g h e d p o i n s$ $G = b a r y {(A, a), (B, b), (C, c)} \Leftrightarrow a G \vec{A} + b G \vec{B} + c G \vec{C} = \vec{0}$ $I \vec{A} + I \vec{B} = \vec{0} \Leftrightarrow I = b a r y {(A, 1), (B, 1)}$
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