a) Ta thấy:[tex]\widehat{OAM}+\widehat{O'AN}=90^o[/tex]
Ta có:[tex]\widehat{AOM}+\widehat{AO'N}=180^o-2\widehat{MAO}+180^o-2\widehat{NAO'}=360^o-2(\widehat{OAM}+\widehat{O'AN})=360^o-180^o=180^o\Rightarrow OM//ON[/tex]
b) Vẽ O'I vuông với OM.
Ta có:[tex]S_{OMNO'}=\frac{O'I(OM+O'N)}{2}=\frac{O'I(R+R')}{2}\leq \frac{OO'(R+R')}{2}[/tex]
Dấu "=" xảy ra khi [tex]OO'\perp OM[/tex]