Question

the bisector of base angle of a triangle enclose a right angle in any case​

Answer 1

ɪɴ ∆ABC , BO and CO are bisecters of B and C respectively.

Now, in ∆ABC,

A + B + C = 180°

B + C = 180° - A................(1)

Now, in ∆BOC

BOC + ½B + ½C = 180°

BOC + ½ ( B + C ) = 180°

BOC + ½ ( 180 - A ) = 180°

BOC = 180° - 90° + ½A

BOC = 90° + ½A

BOC > 90°

Thus it is proved that the bisector of base angle of a triangle cannot enclose a right angle.