Question

va rog repede dau coroanaaa​

Answer 1

 

$\displaystyle\bf\\Se~da:\\Un~cerc\\Punctele ~A,~B,~C~pe~cerc~astfel~incat~AB~este~un~diametru.\\Perpendiculara~in~punctul~A~pe~dreapta~BA\\intersecteaza~dreapta~BC~in~punctul~D.\\AC=12~cm\\CD=9~cm\\\\Se~cere:\\Lungimea~cercului=~?\\\\Rezolvare:\\\\Triunghiul~inscris~in~cerc~care~are~una~din~laturi~diametru~\\este~triungi~dreptunghic.\\\\\implies~m(\sphericalangle ACB)=90^o\\\implies~AC\perp BD\\\implies~\underline{AC~este~inaltime~in~\Delta ABD}$

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$\displaystyle\bf\\Ne~ocupam~de~\Delta ACD\\AC=12~cm\\CD=9~cm\\m(\sphericalangle ACD)=90^o\\Aplicam~Pitagora:\\AD=\sqrt{AC^2+CD^2}=\sqrt{12^2+9^2}=\sqrt{144+81}=\sqrt{225}=15~cm$

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$\displaystyle\bf\\Ne~ocupam~de~\Delta ABD\\AD=15~cm~=cateta\\AB=cateta\\AC=12~cm=inaltime\\CD=9cm\\Teorema~inaltimii\\AC^2=BC\times CD\\\\BC=\frac{AC^2}{CD}=\frac{12^2}{9}=\frac{144}{9}=16~cm\\\\ In~acelasi~triunghi:\\BD=BC+CD=16+9=25~cm\\Teorema~lui~pitagora\\\\AB=\sqrt{BD^2-AD^2}=\sqrt{25^2-15^2}=\sqrt{625-225}=\sqrt{400}=20~cm\\\\AB~este~diametrul~cercului.\\Lc=AB \times \pi = 20\pi~cm\\\\Raspuns~corect~a)$