In an isosceles triangle ABC, with AB=AC, the bisectors of ∠B and ∠C intersect each other at O. Join A to O. Show that : (i) OB=OC (ii) AO bisects ∠A

ΔABC is isosceles, with AB = AC and OB and OC as bisectors of angles B and C, respectively.

To prove that i) OB = OC ii) AO bisects ∠A

Let's put together a diagram to answer the question

<img alt="alt=" triangle"="" class="img-reponsive" loading="lazy" title="triangle" data-cke-saved-src="https://apiengine3.home-tution.com/webroot//files/TRIANGLE.png" src="https://apiengine3.home-tution.com/webroot//files/TRIANGLE.png">

Hence, it is prove that i) OB = OC ii) AO bisects ∠A.