a)[tex]m(\widehat{AOB})=120 \Rightarrow m(\widehat{OAB})=m(\widehat{OBA})=30\\
\cos 30=\dfrac{\dfrac{AB}{2}}{10}=\dfrac{\sqrt{3}}{2} \Rightarrow AB=10\sqrt{3}[/tex]
b)[tex]tg \; 30=\dfrac{6}{\dfrac{AB}{2}}=\dfrac{\sqrt{3}}{3} \Rightarrow AB=12\sqrt{3}[/tex]
c)[tex]m(\widehat{AOB})=90 \Rightarrow AB=r\sqrt2 \Rightarrow AB=10\sqrt2[/tex]
d)[tex]\sin30=\dfrac{h}{10}=\dfrac{1}{2}\Rightarrow h=5\\
A_{\Delta AOB}=\dfrac{AB}{2}\cdot5=25\sqrt3\Rightarrow AB=10\sqrt3[/tex]
