`@Mon`
`a)Xét` `\triangleOBD` `và` `\triangleOAC` `có:`
`OB=OA`
`\hat{O} chung`
`OD=OC`
`=>\triangleOBD=\triangleOAC(c.g.c)`
`=>\hat{OBD}=\hat{OAC};\hat{ODB}=\hat{OCA}`
`=>\hat{IAD}=\hat{IBC};\hat{ADI}=\hat{BCI}`
`Mà` `OA=OB=>OD-OA=OC-OB`
`Và` `OD=OC=>AD=BC`
`Xét` `\triangleADI` `và` `\triangleBCI` `có:`
`\hat{IAD}=\hat{IBC}`
`AD=BC(cmt)`
`\hat{ADI}=\hat{BCI}`
`=>\triangleADI=\triangleBCI(g.c.g)`
`=>AI=BI`
`b)Xét` `\triangleOAI` `và` `\triangleOBI` `có:`
`OA=OB`
`IA=IB`
`OA` `là` `cạnh` `chung`
`=>\triangleOAI=\triangleOBI(c.c.c)`
`=>\hat{AOI}=\hat{BOI}`
`Mà` `\hat{AOI}=\hat{BOI}`
`=>\text{ OI là phân giác}` `\hat{AOB}`
`=>\text{ OI là phân giác}` `\hat{xOy}(đpcm)`
