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

Question

Philoid · Accepted Answer

In sum of all angles of a triangle is 180^o

∠A + ∠B + ∠C = 180^o

Divide both sides by 2, we get

∠A + ∠B + ∠C = 180^o

∠A + ∠OBC + ∠OCB = 90^o [Therefore, OB, OC bisects ∠B and ∠C]

∠OBC + ∠OCB = 90^o - ∠A

Now, in

∠BOC + ∠OBC + ∠OCB = 180^o

∠BOC + 90^o - ∠A = 180^o

∠BOC = 90^o - ∠A

Hence, bisector open base angle cannot enclose right angle.