Question

In a triangle ABC ,it is given that AB = AC and the bisectors of ∠ B and ∠ c intersect at O.If M is a point on BO produced then what conclusion I can make from this​

Answer 1

Step-by-step explanation

In a △ABC, it is given that AB=BC and the bisectors of ∠B and ∠C intersect at O. If M is a point on BO produced, prove that ∠MOC=∠ABC

..

As angles opposite to two equal

sides of a triangle are equal.

⇒∠ABC=∠ACB(AB=AC)

⇒∠B=∠C

Given, OB and OC are bisector of ∠B,∠C

In △OBC,

∠BOC+

2

∠B

+

2

∠C

=180

∘

⇒∠BOC+2×(

2

∠B

)=180

∘

(∠B=∠C)

⇒∠BOC+∠B=180

∘

⇒∠BOC=180

∘

−∠B

As ∠MOC+∠BOC=180

∘

(Linear angles)

⇒∠MOC=180

∘

−∠BOC

⇒∠MOC=180−(180−∠B)

⇒∠MOC=180−180+∠B

⇒∠MOC=∠B

⇒∠MOC=∠ABC

solution........

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