[tex]\it Ducem\ BD\perp AC,\ D\in AC.\\ \\ \Delta ABD - dreptunghic\ isoscel,\ not\breve am\ DA=DB=x\\ \\ Teorema\ lui\ Pitagora\ \Rightarrow x^2+x^2=10^2 \Rightarrow\ 2x^2=100\Big|_{:2} \Rightarrow\ x^2=50 \Rightarrow\ \\ \\ \Rightarrow\ x=\sqrt{50}=\sqrt{25\cdot2}=5\sqrt2\ cm \Rightarrow\ DA=DB=5\sqrt2cm\\ \\ Teorema\ unghiului\ de \ 30^o\ \hat\imath n\ \Delta DBC \Rightarrow\ BC=2\cdot BD=2\cdot5\sqrt2=10\sqrt2\ cm[/tex]
