Răspuns:
c)
Explicație pas cu pas:
∢ABC = 30° =>
AB = 2×AD = 2×6√3 = 12√3 cm
BD² = AB²-AD² = (12√3)²-(6√3)² = 324
=> BD = 18 cm
AD² = BD×DC <=> (6√3)² = 18×DC
=> DC = 6 cm
BC = BD+DC = 18+6 => BC = 24 cm
AD || EC =>
ΔABD ~ ΔEBC
[tex]\frac{BD}{BC} = \frac{AD}{EC} \iff \frac{18}{24} = \frac{6 \sqrt{3} }{EC} \\ EC = \frac{24 \times 6 \sqrt{3} }{18} \implies EC = 8 \sqrt{3} \ cm[/tex]
