Question

Se considera triunghiul ABC cu AB=12 cm si AC=18 cm iar M un punct pe latura [AB] astfel incat AM=8 cm si paralela prin M la latura [BC] intersecteaza latura [AC] in punctul N.Lungimea segmentului [CN] este egala cu...?

Answer 1

[tex]MN||BC\stackrel{T.Thales}{\Longrightarrow}\ \dfrac{AM}{MB}=\dfrac{AN}{NC}\ \stackrel{derivare}{\Longrightarrow}\ \dfrac{AM}{MB+AM} = \dfrac{AN}{NC+AN}\\\;\\ \Rightarrow \dfrac{AM}{AB}=\dfrac{AN}{AC} \Rightarrow \dfrac{8}{12}=\dfrac{AN}{18}\RightarrowAN+ \dfrac{18\cdot8}{12} \Rightarrow AN=12 \ cm.\\\;\\ CN=AC-AN=18-12=6\ cm.[/tex]