[tex]\it BC=6\ cm\ \ \ \ \ \ (1)\\ \\ \mathcal{P}=AB+BC+AC=18 \Rightarrow AB+6+AC=18|_{-6} \Rightarrow AB+AC=12\ \ \ \ (2)\\ \\ I)\ AB=AC\ \stackrel{(2)}{\Longrightarrow} AB=AC= 6 cm\ \ \ \ \ (3)\\ \\ (1),\ (3) \Rightarrow AB=BC=AC=6\ cm \Rightarrow \Delta ABC-echilateral \Rightarrow \widehat{ABC}=60^o\\ \\ \\ II)\ AB=BC=6\ \stackrel{(2)}{\Longrightarrow} AC= 6 cm \Rightarrow AB=BC=AC=6\ cm \Rightarrow \\ \\ \Rightarrow\Delta ABC-echilateral \Rightarrow \widehat{ABC}=60^o[/tex]
[tex]\it III)\ AC=BC=6\ \stackrel{(2)}{\Longrightarrow} AB= 6 cm \Rightarrow AB=BC=AC=6\ cm \Rightarrow \\ \\ \Rightarrow\Delta ABC-echilateral \Rightarrow \widehat{ABC}=60^o[/tex]
