In the figure, `OD` is the bisector of `/_``AOC`, `OE` is the bisector of `/_``BOC` and `OD` `bot` `OE`. Show that the points `A`, `O` and `B` are collinear.

Explanation

Given In the figure, OD `bot`OE,OD and OE and bisectors of `/_`AOC and `/_BOC`.
To show Points A, O and B are collinear i.e., AOB is a straight line.
Proof Since, OD and OD and OE bisect angles `/_`AOC and `/_`BOC, repectively.
`:." "/_AOC = 2 /_DOC`
and `" " /_COB = 2 /_COE`
On adding Equ. (i) and (ii), we get
and` " " /_COB = 2 /_COE`
`rArr " "/_AOC + /_COB = 2 /_(DOC + /_COE)`
`rArr" "/_AOC + /_COB = 2 /_DOC `
`rArr" "/_AOC + /_COB = 2xx90^(@)`
`rArr" "/_AOC + /_COB = 180^(@)`
`:." "/_AOB = 180^(@)`
So, `/_AOC and /_`COB are forming linear pair.
Also, AOB is a straight line.
Hence, point A, O and B are collinear.