Question

the bisector of angle B and angle C of an isosceles triangle with ab is equal to AC intersect each other at point O. OB is produced to meet AC at a point M and prove that angle moc is equal to angle abc​

Answer 1

Step-by-step explanation:

Given:

Lines OB and OC are the bisectors of ∠B and ∠C of an isosceles ΔABC such that AB=AC which intersect each other at O and BO is produced to M.

 

To prove:

∠MOC=∠ABC

 

Consider the diagram shown below.

 

Proof:

 In ΔABC,

AB=AC    (given)

∠ACB=∠ABC      (angles opposite to equal sides are equal)

21∠ACB=21∠ABC      (dividing both sides by 2)

 

Therefore,

∠OCB=∠OBC    …… (1)

(Since, OB and OC are the bisector of ∠B and ∠C)

 

Now, from equation (1), we have

∠MOC=∠OBC+∠OBC

 ∠MOC=∠OBC

 ⇒∠MOC=2∠ABC

(Since, OB is the bisector of ∠B)

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Answer 2

Answer:

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this is solution from page number 287