E complicat de demonstrat formula doar cu teorema lui Pythagora, deci doar o sa iti spun formula asa cum este.
[tex]AM^{2}=\frac{2(AB^{2}+AC^{2})-BC^{2}}{4}\Rightarrow 2(AB^{2}+AC^{2})=4AM^{2}+BC^{2}\Rightarrow AB^{2}+AC^{2}=\frac{4AM^{2}+BC^{2}}{2}\Rightarrow 16+AC^{2}=\frac{4*25+144}{2}\Rightarrow AC^{2}=\frac{244}{2}-16=122-16=106\Rightarrow AC=\sqrt{106}[/tex]
