Question

BO and CO are respectively the bisector of Angle B and Angle C of triangle ABC. AO produced meets BC at P, then find AB/AC.

Answer 1

 In ΔABP

BO is the bisector of ∠B

by the theorem of angle bisector;

AB/BP = AO/OP

in the ΔACP

by the theorem of angle bisector

AC/CP = AO/ OP

comparing equation 1 & equation 2

AB/BP = AC/CP

or AB/AC = BP/CP

Answer 2

Given: ABC is a triangle, and BO and CO are the angle bisector of Angle B and Angle C 

In the triangle ABP 

BO is the angle bisector of Angle B 

So we will apply the angle bisector theorem 

AB/BP = AO/OP (this is equation 1) 

And for the angle ACP 

Bisector therom will be  

AC/CP = AO/OP (this is equation 2) 

We will compare the both equations 

AB/BP=AC/CP ===> AB/AC=BP/CP