Răspuns:
[tex]\boxed{\mathbf{m(\angle{AMB})=150^{\circ}}}[/tex]
Explicație pas cu pas:
[tex]\mathbf{In\: cercul\: C(O\,;r)\: avem:}[/tex]
[tex]\mathbf{AB=6\,cm\,(coarda)}[/tex]
[tex]\mathbf{r=6cm \implies BO=AO=6\,cm}[/tex]
[tex]\mathbf{In\: triunghiul\:\triangle\: AOB\: avem:}[/tex]
[tex]\mathbf{AB=6cm\, , AO=6cm\,, BO=6cm \implies \triangle AOB-echilateral}[/tex]
[tex]\mathbf{\triangle AOB-echilateral \implies \hat{A}=\hat{B}=\hat{O}=60^{\circ}}[/tex]
[tex]\mathbf{\implies m(\widehat{AB})=60^{\circ}(unghi\:la\:centru)}[/tex]
[tex]\mathbf{C(O\,;r)=360^{\circ}\implies \widehat{ANB}=360^{\circ}-60^{\circ}=300^{\circ} ,unde\:N \in C(O\,;r)\:si\: N \in ext\: \widehat{AB}}[/tex][tex]\mathbf{M \in \widehat{AB} \implies m(\angle {AMB})=\dfrac{\widehat{ANB}}{2}=\dfrac{300^{\circ}}{2}= \boxed{\mathbf{150^{\circ} }} }[/tex]
