[tex]\it \widehat B =60^o\ (complementul \ lui \ 30^o)\ \ \ \ \ (1)\\ \\ AE-median\breve a\ corespunz\breve atoare\ ipotenuzei \Rightarrow AE=\dfrac{BC}{2} \Rightarrow AE=BE \Rightarrow \\ \\ \\ \Rightarrow \Delta BEA-isoscel\ \ \ \ (2)\\ \\ \\ (1),\ (2) \Rightarrow \Delta BEA-echilateral\ \ \ \ \ (3)\\ \\ \\ AD-\hat\imath n\breve al\c{\it t}ime\ \stackrel{(3)}{\Longrightarrow}\ AD-median\breve a \Rightarrow BD=DE=3cm\\ \\ \\ BE=BD+DE=3+3=6cm \Rightarrow \dfrac{BC}{2}=6cm \Rightarrow BC=2\cdot6=12\ cm[/tex]
