[tex]\it \Delta ABC-dreptunghic\ isoscel,\ m(\hat A)=90^o,\ \ m(\hat B)= m(\hat C)=45^o\\ \\ \Delta CNP-dreptunghic\ isoscel \Rightarrow CN = NP\ \ \ \ (1)\\ \\ AMPN-dreptunghi \Rightarrow NP=AM\ \ \ \ (2)\\ \\ (1).\ (2) \Rightarrow AM=CN\ \ \ \ (3)\\ \\ AM+AN\stackrel{(3)}{=}\ CN+AN=AC=10\ cm[/tex]