[tex]\bf C(O;r)=360^{\circ}\implies \widehat{AB}+\widehat{BC}+\widehat{CA}=360^{\circ}[/tex]
[tex]\bf O \subset \angle AOB \implies \angle AOB - \angle \: la \; centru[/tex]
[tex]\bf \implies \widehat{AB}=\angle AOB=60^{\circ}[/tex]
[tex]\bf x\% \; din \; 360^{\circ}=60^{\circ}[/tex]
[tex]\bf \implies \dfrac{x}{100} \cdot 360^{\circ}=60^{\circ}\implies \dfrac{x}{10} \cdot 36 =60\;|\cdot 10[/tex]
[tex]\bf \implies 36x=600\; |:36 \implies \boxed{\bf x=16,(6)\%} \;(a)[/tex]
[tex]\bf O \subset \angle BOC \implies \angle BOC - \angle \: la \; centru[/tex]
[tex]\bf \implies \widehat{BC}=\angle BOC = 90^{\circ}[/tex]
[tex]\bf x\% \; din \; 360^{\circ}=90^{\circ}[/tex]
[tex]\bf \implies \dfrac{x}{100} \cdot 360 = 90 \implies \dfrac{x}{10} \cdot 36=90 \; |\cdot 10[/tex]
[tex]\bf \implies 36x=900\; | :36 \implies \boxed{\bf x=25\%}\; (b)[/tex]
[tex]\bf \angle COD \leq 180^{\circ}[/tex]
[tex]\bf 50\% \: din \; 360^{\circ}=\angle COD = x[/tex]
[tex]\bf \implies \dfrac{50}{100}^{(50} \cdot 360=x \implies \dfrac{1}{2} \cdot 360=x[/tex]
[tex]\bf \implies x=\dfrac{360^{\circ}}{2} \implies \boxed{\bf x=180^{\circ}}\; (c)[/tex]
Bafta! :)
#copaceibrainly
