Question

if the bisector of angles ABC & ACB of a triangle ABC meet at a point O, then prove that angle BOC = 90 + 1/2 angle A?​

Answer 1

ANSWER

Given :

A △ABC such that the bisectors of ∠ABC and ∠ACB meet at a point O.

To prove :

∠BOC=90o+21∠A

Proof :

In △BOC,

∠1+∠2+∠BOC=180o

In △ABC,

∠A+∠B+∠C=180o

∠A+2(∠1)+2(∠2)=180o

2∠A+∠1+∠2=90o

∠1+∠2=90o−2∠A

Therefore,

90o−2∠A+∠BOC=180o

∠BOC=90o+2∠A

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