Question

Pe laturile AB si AC ale triunghiului ABC se considera punctele M, respectiv N, astfel incat MN || BC. Folosind informatii din Figurile 20-21, determina lungimile segmentelor indicate:​

Answer 1

$\it MN||AB\ \stackrel{T.f.a.}{\Longrightarrow}\ \Delta ABC\sim\Delta MNC \Rightarrow k=\dfrac{AB}{MN}=\dfrac{30}{20}=\dfrac{3}{2}\ (raport\ de\ asem.)\\ \\ \\ \dfrac{BC}{NC}=\dfrac{3}{2} \Rightarrow \dfrac{BC}{12}=\dfrac{3}{2} \Rightarrow BC=\dfrac{3\cdot12}{2}=\dfrac{36}{2}=18\ cm\\ \\ \\ BN=AB-NC=18-12=6\ cm\\ \\ \\ MN||AB\ \stackrel{T.Thales}{\Longrightarrow}\ \dfrac{CM}{MA}=\dfrac{CN}{NB} \Rightarrow \dfrac{CM}{7}=\dfrac{12}{6} \Rightarrow\dfrac{CM}{7}=2 \Rightarrow CM=7\cdot2=14$