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Question Number 177769 by a.lgnaoui last updated on 08/Oct/22

$$determinerleselementsdemandes$$$$danslegraphe$$

Commented by a.lgnaoui last updated on 08/Oct/22

Commented by a.lgnaoui last updated on 09/Oct/22

$$\measuredangle \mathrm{ADB}=180-(65+70)=45$$$$\measuredangle \mathrm{BDC}=45\Rightarrow \measuredangle \mathrm{ADC}=90$$$$\mathrm{Donc}△\mathrm{ADC}\mathrm{triangle}\mathrm{rectangle}$$$$\mathrm{doonc}\mathrm{AC}\mathrm{passe}\mathrm{par}\mathrm{centre}\mathrm{du}\mathrm{cercle}$$$$\mathrm{AC}=\mathrm{diametre}$$$$\mathrm{ACB}\mathrm{aussi}\mathrm{triangle}\mathrm{rectangle}$$$$\mathrm{donc}\measuredangle \mathrm{DBC}=90-70=20$$$$\mathrm{Donc}\measuredangle \mathrm{BCD}=180-(45+20)=115$$

Answered by Ar Brandon last updated on 08/Oct/22

$$\mathrm{\Delta }\mathrm{OAB}\equiv \mathrm{\Delta }\mathrm{OCD}$$$$\Rightarrow \mathrm{\angle }\mathrm{OCD}=\mathrm{\angle }\mathrm{OBA}=70°$$$$\Rightarrow \mathrm{\angle }\mathrm{OAB}=\mathrm{\angle }\mathrm{ODC}=45°$$$$\Rightarrow \mathrm{\angle }\mathrm{OAD}=65°-\mathrm{\angle }\mathrm{OAB}=20°$$$$\Rightarrow \mathrm{\angle }\mathrm{AOB}=180°-70°-45°=65°$$$$\Rightarrow \mathrm{\angle }\mathrm{BOC}=180°-\mathrm{\angle }\mathrm{AOB}=115°$$$$\mathrm{\Delta }\mathrm{OBC}\equiv \mathrm{\Delta }\mathrm{OAD}$$$$\Rightarrow \mathrm{\angle }\mathrm{OBC}=\mathrm{\angle }\mathrm{OAD}=20°$$$$\Rightarrow \mathrm{\angle }\mathrm{OCB}=180°-\mathrm{\angle }\mathrm{BOC}-\mathrm{\angle }\mathrm{OBC}=45°$$$$\left(i\right)\mathrm{\angle }\mathrm{BCD}=\mathrm{\angle }\mathrm{OCB}+\mathrm{\angle }\mathrm{OCD}=45°+70°=115°$$$$\left(ii\right)\mathrm{\angle }\mathrm{ADB}=\mathrm{\angle }\mathrm{OCB}=45°$$

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