Question

In a isosceles triangle ABC with AB=AC the bisectors of the bisectors of Angle B and angle C intersect each other at O. joint AtoC show that:
1).OB=OC
2).AO bisects angle A

Answer 1

Here's your answer!!

Solution:-

i) It's given that ,

ABC is a isosceles triangle .

So,

=>AB =AC

(Since angle opposite to equal sides are equal .)

So,

=> <B = <C

Therefore,

$= > \frac{1}{2} < b = \frac{1}{2} < c$

That is ,

=> <OBC =<OCB

(Since sides opposite to equal angle are also equal.)

So,

=>OB =OC ...... 1st Proved !

ii) In ∆ABO and ∆ACO,

=> AB = AC (Given )

=>OB =OC (Proved above)

=> AO = OA (Common)

Hence ,

=> ∆ABO is congruent to ∆ACO

And hence,

=> <BAO = <CAO (By C.p.c.t)

Hence, AO bisect <A

Hope it helps you!! ^^

#Be Brainly