مرکزی $E\widehat{O}D=45\Rightarrow \overset\frown{ED}=45{}^\circ $  خارجی $\widehat{A}=\frac{\overset\frown{DE}-\overset\frown{BC}}{2}\,\,\,\,\,\,\,\,\left( 1 \right)$ $AB=\underbrace{OD=OB=OE}_{{}}$ $\Rightarrow \overset{\Delta }{\mathop{OBA}}\,$  متساوی الساقین $\Rightarrow \widehat{A}=B\widehat{O}C=\overset\frown{BC}$  $\left( 1 \right)\Rightarrow \frac{45-\overset\frown{BC}}{2}=\overset\frown{BC}\Rightarrow 45=3\overset\frown{BC}\Rightarrow \overset\frown{BC}=15$  $B\widehat{A}O=\frac{45-15}{2}=15$