KZ-MO 2008 Problem 2

Suppose that $B_1$ is the midpoint of the arc $AC$ , containing $B$ , in the circumcircle of $\triangle ABC$ , and let $I_b$ be the $B$ -excircle's center. Assume that the external angle bisector of $\angle ABC$ intersects $AC$ at $B_2$ . Prove that $B_2I$ is perpendicular to $B_1I_B$ , where $I$ is the incenter of $\triangle ABC$ .