Question

In a triangle ABC the internal bisectors of Angle B and angle C meet at O prove that OA is the internal bisector of angle A

Answer 1

Given : In a triangle ABC the internal bisectors of Angle B and angle C meet at O  

To find :  prove that OA is the internal bisector of angle A

Solution:

Lets draw a line from A passing through O  meeting BC at  D

in Δ ABD  

BO is angle bisector

Hence  AB / BD =  AO/OD   ( internal bisector theorem )

in Δ ACD  

CO is angle bisector

Hence  AC / CD =  AO/OD  ( internal bisector theorem )

Equating Both

AB / BD = AC / CD

=> AB/ AC  = BD/CD

Hence  AD is angle bisector of ∠A in Δ ABC  ( Converse of internal bisector theorem )

O lies on AD

Hence  OA is internal bisector of ∠A

QED

Hence proved

Learn More:

In the given figure AD is internal bisector of angle A and CE is ...

https://brainly.in/question/11611726

The interior angle bisector of angle B, and the exterior bisector of ...

https://brainly.in/question/13087951

Answer 2

Answer:

Dfh us did stfu office

off sa

s

s

da

s

f

r

s

the

the d

s

g

flora d

h

r

fy

u

yr

d

g

h

yydoekrtt

r

t

y

yyyy

y

y

y

y

y

r

r

r

t

y

h

h

fr