Question

Dau 60 de puncte .........

Answer 1

   
[tex]\displaystyle\\ _\texttt{Daca 3 sau mai multe paralele, la distante diferite intre ele, sunt taiate }\\ _\texttt{de 2 sau mai multe secante inclinate la unghiuri diferite, se formeaza pe}\\ _\texttt{secante segmente proportionale.}\\\\ \text{Exemple pe desenul dat:}\\\\ \frac{AE}{ED} = \frac{BF}{FC} ~~~{\bf sau}\\\\ \frac{AE}{AD} = \frac{BF}{BC} [/tex]

[tex]\displaystyle\\ \texttt{Rezolvare:}\\\\ \frac{AE}{ED} = \frac{3}{5}\\\\ \text{Facem proportia derivata.}\\\\ \frac{AE}{AE+ED} = \frac{3}{3+5}~~~\Longleftrightarrow~~~\frac{AE}{AD} = \frac{3}{8}\\\\ \Longrightarrow~~\frac{AE}{AD} =\frac{BF}{BC} = \frac{3}{8}~~\text{ unde BC = 16 cm.}\\\\ \Longrightarrow~~\frac{BF}{16} = \frac{3}{8}\\\\ \Longrightarrow~~ BF = \frac{16\times 3}{8}= 2\times 3 = \boxed{\bf 6~cm} \\\\ \Longrightarrow~~ FC = BC - BF = 16 - 6 = \boxed{\bf 10~cm} [/tex]