a) Ta có: \(\widehat{AOD}=\widehat{AOC}-\widehat{DOC}=90-\widehat{DOC}\)(1)
\(\widehat{BOC}=\widehat{BOD}-\widehat{DOC}=90-\widehat{DOC}\)(2)
Từ (1)(2) => \(\widehat{AOD}=\widehat{BOC}\)(đpcm)
b) Ta có: OM phân giác góc DOC => \(\widehat{DOM}=\widehat{COM}\)
Mà \(\widehat{AOD}=\widehat{BOC}\)(c/m a) => \(\widehat{AOD}+\widehat{DOM}=\widehat{BOC}+\widehat{COM}\)
\(\Leftrightarrow\widehat{AOM}=\widehat{BOM}\)
=> OM phân giác góc AOB