The bisectors of base angles of a triangle cannot enclose a right angle in any case.

Explanation

In `/_\ABC`, `BO` and `CO` are bisectors of `angleB` and `angleC` respectively.
Now, in `△ABC`,
`/_A+/_B+/_C=180°`
`/_B+/_C=180°−/_A` .....(1)
Now, in `/_\BOC`,
`/_BOC+1/2/_B+1/2/_C=180°`
`/_BOC+1/2(/_B+/_C)=180°`
`/_BOC+1/2(180°−/_A)=180°`
`=>/_BOC=180°−90°+1/2/_A`
`=>/_BOC=90°+1/2/_A`
`=>/_BOC>90°`
Thus it is proved that the bisector of base angles of a triangle cannot enclose a right angle.