[tex]\it Not\breve am\ \ BD=x \Rightarrow BC=4x\\ \\ Th.\ catetei \Rightarrow AB^2=BD\cdot BC \Rightarrow 12^2=x\cdot 4x \Rightarrow 12^2=4x^2 \Rightarrow \\ \\ 4x^2=12^2 \Rightarrow (2x)^2=12^2 \Rightarrow 2x=12|_{\cdot2} \Rightarrow 4x=24 \Rightarrow BC=24\ cm\\ \\ Reciproca\ Th.\ \angle30^o \Rightarrow \widehat C=30^o\\ \\ cosC=\dfrac{AC}{BC} \Rightarrow cos30^o=\dfrac{AC}{24} \Rightarrow AC=24\cdot cos30^o=24\cdot\dfrac{\sqrt3}{2}=12\sqrt3cm[/tex]
