[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]
