Question

In ∆ABC, AB = AC, and the bisectors of angles B and C intersect at point O. Prove that BO = CO and the ray AO is the

bisector of angle BAC.

Answer 1

first draw the diagram as given in inst from the question,
then visualize what i say;

in triangle abc ab=ac
which gives angle acb=angle abc
[equal sides of an isoceles triangle subtends equal angles opp to them]

now angle ocb=angle obc
[ oc &ob are angle bisector of acb &abc]

hence ob =oc
[by the converse of isoceles riangle property i jst gave above]

sry no proof for the ao and bisecter bac part :)

Answer 2

as it is given that ab=ac so...∠B = ∠ C{because angles opposite to equal sides r equal}
if ∠ b =∠ c ...so ∠obc=∠ocb 
so BO=CO{because angles opposite to equal sides r equal}