Question

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Answer 1

Answer:

Let BP and CP are bisector of angles B and C respectively

we need to prove that bisectors of the base angles of a triangle can never enclose a right angle.

In △ABC,∠A+∠B+∠C=180

∘

Now ∠A+2∠1+2∠C=180

∘

2(∠1+∠2)=180

∘

−∠A

⇒∠1+∠2=90

∘

−

2

∠A

In △PBC,∠P+∠1+∠2=180

∘

∠P+90

∘

−

2

∠A

=180

∘

∠P=90

∘

+

2

∠A

Hence angle P is always greater then 90

∘

Thus PBC can never be a right angled triangle