question_answer

In the given triangle ABC, the sides AB and AC are produced to P and Q, respectively. The bisector of \[\angle PBC\] and \[\angle QCB\] intersect at O then \[\angle BOC\] is equal to:

A)  \[90{}^\circ +\frac{\angle A}{2}\]                    

B)  \[90{}^\circ -\frac{\angle A}{2}\]

C)  \[90{}^\circ -\frac{\angle A}{4}\]                      

D)  \[45{}^\circ +\frac{\angle A}{2}\]

E)  None of these