[tex]\bf a)\;Fie \; in\; C(O;r) : OC-raza[/tex]
[tex]\bf BO;CO-raze \implies BC-diametru[/tex]
[tex]\bf Stiim \; ca \; masura\; \angle \; opus \; diametrului \; in semicerc \; este\; de \; 90^{\circ}[/tex]
[tex]\bf \implies \angle A=90^{\circ}[/tex]
[tex]\bf \widehat{AC}=40^{\circ} \implies \angle B=\dfrac{\widehat{AC}}{2} =\dfrac{40^{\circ}}{2} =20^{\circ}[/tex]
[tex]\bf \implies \angle C=180^{\circ}-\angle A-\angle B=180^{\circ}-90^{\circ}-20^{\circ}=70^{\circ}[/tex]
[tex]\star[/tex]
[tex]\bf b)\; \widehat{AB}=60^{\circ} \implies \angle C=\dfrac{\widehat{AB}}{2} =\dfrac{60^{\circ}}{2}=30^{\circ}[/tex]
[tex]\bf \widehat{AC}=70^{\circ} \implies \angle B=\dfrac{\widehat{AC}}{2} =\dfrac{70^{\circ}}{2} =35^{\circ}[/tex]
[tex]\bf \implies \angle A=180^{\circ}-\angle B-\angle C=180^{\circ}-35^{\circ}-30^{\circ}=115^{\circ}[/tex]
[tex]\star[/tex]
[tex]\bf c)\;BC-diametru \implies \angle A=90^{\circ}[/tex]
[tex]\bf AB \equiv AC \implies \triangle ABC-isoscel[/tex]
[tex]\bf \implies \angle B=\angle C=x^{\circ}[/tex]
[tex]\bf Stim \; ca \; \angle A + \angle B + \angle C=180^{\circ}[/tex]
[tex]\bf \implies 90^{\circ}+x+x=180 \implies 2x+90^{\circ}=180^{\circ}[/tex]
[tex]\bf \implies 2x=180^{\circ}-90^{\circ}=90^{\circ}\:|:2[/tex]
[tex]\bf \implies \angle B=\angle C=45^{\circ}[/tex]
[tex]\star[/tex]
Bafta!
#copaceibrainly
