\(a,\left\{{}\begin{matrix}AE=AB\\\widehat{BAO}=\widehat{EAO}\\AO\text{ chung}\end{matrix}\right.\Rightarrow\Delta OAE=\Delta OAB\left(c.g.c\right)\\ \Rightarrow OE=OB\\ b,\text{Gọi }\left\{H\right\}=OA\cap BE\\ \Rightarrow\left\{{}\begin{matrix}AE=AB\\\widehat{BAH}=\widehat{EAH}\\AH\text{ chung}\end{matrix}\right.\Rightarrow\Delta HAE=\Delta HAB\left(c.g.c\right)\\ \Rightarrow\left\{{}\begin{matrix}HE=HB\\\widehat{AHE}=\widehat{AHB}\end{matrix}\right.\\ \text{Mà }\widehat{AHE}+\widehat{AHB}=180^0\\ \Rightarrow\widehat{AHE}=90^0\\ \Rightarrow AH\bot BE\\ \text{Mà }HE=HB\Rightarrow AH\text{ hay }AO\text{ là trung trực }BE\)
\(c,\widehat{ABO}=\widehat{AEO}\Rightarrow180^0-\widehat{ABO}=180^0-\widehat{AEO}\\ \Rightarrow\widehat{OBD}=\widehat{OEC}\\ \text{Mà }\widehat{BOD}=\widehat{EOC}\left(đđ\right);OB=OE\\ \Rightarrow\Delta OBD=\Delta OEC\left(g.c.g\right)\\ \Rightarrow BD=EC\\ \Rightarrow AB+BD=EC+AE\\ \Rightarrow AC=BD\)
