a) AB=AC=>ABC isoscel=>m(∡C)=45=>ADC isoscel=>AD=DC
m(∡B)=45=>ADB isoscel=>AD=BD
BC=BD+DC=2AD=12cm
[tex] AB^{2}+ AC^{2}= BC^{2} [/tex]=>2[tex] AB^{2}= 12^{2}=144=\ \textgreater \ AB^{2}=72=\ \textgreater \ AB=6 \sqrt{2} [/tex]
b)BC=BD+DC=BD+2BD=3BD=27=>BD=9
DC=2BD=18
[tex] AD^{2}=BD*DC [/tex](teorema inaltimii)=>[tex] AD^{2}=9*18= 162=\ \textgreater \ AD=9 \sqrt{2} [/tex]
