[tex]\it \widehat{AOB}=\dfrac{\widehat{BOC}+\widehat{COD}+\widehat{DOA}}{3}|_{\cdot3} \Rightarrow 3\cdot\widehat{AOB}=\widehat{BOC}+\widehat{COD}+\widehat{DOA}|_{+\widehat{AOB}}\Rightarrow\\ \\ \\ \Rightarrow 4\cdot\widehat{AOB} =\widehat{AOB}+\widehat{BOC}+\widehat{COD}+\widehat{DOA} \Rightarrow 4\cdot \widehat{AOB}=360^0|_{:4} \Rightarrow \\ \\ \\ \Rightarrow \widehat{AOB}=90^0 \Rightarrow AC\perp BD \Rightarrow ABCD\ -\ romb[/tex]
