Question

ex 1 va rog mult !!

Answer 1

BA' / A'C = k = 1

AA' = 1/k+1 * AB + k/k+1 * AC

AA' = 1/2 * AB + 1/2 * AC = 1/2 ( AB + AC) = 1/2 ( AB + AB + BC) = (2AB + BC) / 2

AB' / B'C = k = 1

BB' = 1/k+1 * BA + k/k+1 * BC

BB' = 1/2 * BA + 1/2 * BC = 1/2 (BA + BC) = 1/2 ( BC + CA + BC) = ( 2BC + CA)/2

AC' / C'B = k = 1

CC' = 1/k+1 * CA + k/k+1 * CB

CC' = 1/2 * CA + 1/2 * CB = 1/2 (CA + CB) = 1/2( CA + CA + AB) = ( 2CA + AB) /2

Adunam:

AA' + BB' + CC' = 1/2 * AB + 1/2 * BA + 1/2 * AC + 1/2 * CA + 1/2 * BC + 1/2 * CB = 1/2 ( AB + BA + AC + CA + BC + CB) = 1/2 * 0 = 0

dar AA' + BB' + CC' poate fi si :

(3AB + 3BC + 3CA)/2

= 3/2 ( AB + BC + CA ) = 3 /2 ( a + b + c)

Atat! Sper ca a fost de ajutor!