 Hello and welcome to the session. My name is Mansi and I'm going to help you with the following question. The question says in an isosceles triangle ABC with AB equal to AC, the bisectors of angle B and angle C intersect each other at O, join A to O and show that first OB equals to OC and second AO bisects angle A. In this question we are given that AB equals to AC and bisectors of angle B and angle C intersect each other at O. Then we have to join A to O and show the following things. Now before starting with the solution let us see the key idea behind the question. Now here we use the following two theorems. First is angles opposite to equal sides of an isosceles triangle are equal and second theorem is the sides opposite to equal angles of a triangle are equal. Let us now start with the solution to this question. We start with the first part that is we have to prove that OB equals to OC in this triangle. Now in the first part we use the first key idea that is angles opposite to equal sides of an isosceles triangle are equal. We are given that AB equals to AC therefore angle B is equal to angle C or we can say half of angle B is equal to half of angle C or angle OBC is equal to angle OCB or angle ABO equals to angle ACO. This happens because OB and OC are the bisectors of angle B and angle C respectively therefore OB is equal to OC hence proved. Now let us see the solution to the second part that is now we have to prove that AO bisects angle A. Now in triangle ABO and triangle ACO AB is equal to AC that is given to us in the question angle ABO is equal to angle ACO this we have just proved and OB is equal to AC this we did in the last part therefore triangle ABO is congruent to triangle ACO by SAS that is side angle site congruence rule so angle BAO is equal to angle CAO by CPCT that is congruent part of congruent triangles hence AO bisects angle A hence proved. So I hope you understood the question and enjoyed the session have a good day.