[tex]\it CD|| AB \stackrel{T.f.a.}{\Longrightarrow}\ \Delta OAB \sim \Delta OCD \Rightarrow k=\dfrac{AB}{CD}=\dfrac{24}{8}=3\ (raportul\ \ de\ \ asem\breve a nare)\\ \\ \\ \dfrac{OB}{OD}=3 \Rightarrow \dfrac{OB}{OD}=\dfrac{3}{1} \Rightarrow \dfrac{OB}{OD+OB}=\dfrac{3}{1+3} \Rightarrow\\ \\ \\ \Rightarrow \dfrac{OB}{BD}=\dfrac{3}{4} \Rightarrow OB=\dfrac{3\cdot BD}{4}=\dfrac{3\cdot20}{4}=3\cdot5=15\ cm[/tex]
