Răspuns:
d(D, AC) = 1 cm
Explicație pas cu pas:
ΔABC isoscel => AB = AC = 4 cm
D = mij BC => BD = DC = BC/2 => BC = 2·DC
d( D, AC) = ?
In ΔABC:
D = mij BC => AD = mediana, inaltime, bisectoare
AD = inaltime => ∡ADC = 90°
AD = bisectoare => ∡BAD = ∡DAC = ∡BAC / 2 = 30° / 2 = 15°
Vom scrie aria in doua moduri:
A = AB · AC · sin(∡BAC) / 2 = 4 · 4 · [tex]\frac{1}{2}[/tex] · [tex]\frac{1}{2}[/tex] = 4 cm²
A = AD · BC /2
dar BC = 2·DC => A = (AD·2·DC) /2 = AD·DC = 4cm
fie d(D, AC) = DM => DM ⊥ AC
Aria ΔADC :
A = (AD·DC) / 2
dar AD·DC = 4cm => A = 2 cm
dar Aria ΔADC => A = (DM·AC)/2 = 2 cm | ·2
DM · AC = 4
DM · 4 = 4 | :4
DM = 1 cm => d(D, AC) = DM = 1 cm
